Chapter 1

Steady‐State Modeling of Equilibrium Distillation

Vilmar Steffen and Edson Antonio da Silva

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66833

Abstract In this chapter, an algorithm for the solution of the mathematical model featuring steady-state multicomponent distillation columns is analyzed and applied in the case study of the separation of hydrocarbon mixture. The development of the model has assumed each stage outlet streams in thermodynamic equilibrium in the phases liquid and vapor. The modeling of liquid was considerate and the non-ideality behavior was described by activity. The non-ideality of gas phase was calculated by Peng-Robinson equation of state. The model consists of a set of nonlinear algebraic equations. The algorithm and numerical procedure to solve a set of equations are presented in a sequential, general and very simple form. A methodology to produce the good initial guess was defined based on rude simplifications of the system. In the study case, the initial estimates generated by the method are very good, being only about 20% far from the simulation results and considering a tolerance of 10-10, the convergence was obtained with 28 iterations.

The analysis of a plant, by simulation, within the development of new processes may fre-quently show beforehand whether it is technically and economically viable. The simulationprocess in already operating plants may optimize the operational conditions for better qualityproducts, decrease energy consumption and other losses in the process [1].

The design of a multicomponent distillation column by phenomenological models is quite

complex due to the large number of parameters and variables involved [2] and also usually, itis required to solve the set of nonlinear equations and differential equations. Mathematicalmodeling is a powerful and useful tool in the design of this type of equipment, it assists the4 Distillation - Innovative Applications and Modeling

control and optimization column and therefore, the project and operating costs can be signif- icantly reduced. The use of distillation as separation method is disseminated by the modern chemical industry. One can find it in almost all industrial chemical processes where liquid separation is required. Common commercial binary distillations are as follows: water/ethylene glycol, benzene/tolu- ene, o-xylene/m-xylene, isopentane/n-pentane, ethylbenzene/styrene, water/acetic acid, etha- nol/water, among others [2]. There are a lot of hydrocarbons mixtures that can be cited as commercial multicomponent distillation examples. With all the foregoing, it is clear the need to provide the theoretical study on a simplified model for evaluating the possible separation processes using distillation columns. The simplest mathematical model for a distillation column is obtained, considering that all stages outlet streams (liquid and vapor) are in thermodynamic equilibrium. What represents, with no much accuracy, what happens in an actual process; however, this study is very important to get an idea of the theoretically best result that can be achieved in the process in question. Thus, the equations of a distillation column model are obtained from mass and energy balances, mass balances by component and iso-fugacity equations. The equations that represent such model are highly nonlinear, particularly those describing the phase equilibria and energy balances. The solution of a set of nonlinear equations is quite difficult and generally requires that good initial guesses are provided in the way the method presents convergence [3]. Thus, the solution of the obtained model is divided into several steps, where in each step is calculated a set of model unknowns (mole fraction, temperature, flow rate, etc.), such that it is not necessary the solution of nonlinear equations sets, but only sets of linear equations, evaluation of explicit algebraic expressions and root finding of single variable. Also will be presented a methodol- ogy to generate good initial guesses and an example will be studied using the methodology presented. The simplest methods used for solving the modeling of distillation columns are the graphical ones like McCabe-Thiele [4] and Ponchon-Savarit [5, 6]. The equation obtained by modeling the steady state of equilibrium distillation columns forms a set of highly nonlinear equations (MESH equations, obtained from mass and energy balances, phase equilibrium relations and mole fractions summations) that are normally solved all at the same time by Newton-Raphson and like-one method. Another, much used, type of method is that one which uses “tearing equations,” that is, large sparse systems of algebraic equations are split into smaller systems and solved in a sequential form [7–11]; it makes the solution process simpler but, as a conse- quence, can occur some instability. So, the idea of the method being proposed aims to join the efficiency of Newton-Raphson-like methods with the simplicity of methods based on tearing equations, what is possible only with a very good initial estimates generating methodology.

2. Model assumptions

The following assumptions were made when formulating the model of the distillation process: • Steady state; Steady‐State Modeling of Equilibrium Distillation 5 http://dx.doi.org/10.5772/66833

• No reaction occurs in the column;

• The vapor and liquid phases are homogeneous in all stages;• The vapor and liquid leaving any stage are in phase equilibrium;

• The model does not include effects due to column internals (e.g., pressure drops and flooding/weeping).

3. Modeling

The modeling of a steady-state distillation column is based mainly on mass and energybalances; in this way, it is needed to understand the equipment layout to obtain such mathe-matical equations [8, 12, 13]. This model is based on the equations of the column called MESH(material balance equations, phase equilibrium equations, mole fractions summation equa-tions and heat, which means energy balance equations). Aiming to make the model as generalas possible, it will be considered that can exist feed stream in any stage and the output streams(bottoms and distillate) can be in liquid phase, vapor phase or both phases [14]. Figure 1 showsa schematic representation of a distillation column and Figure 2 shows a schematic represen-tation of input and output streams in a stage.Where Fj is the flow rate of the feed stream to stage j, Qj is the heat load from stage j (forconvention, it was assumed the heat leaving the stage), Lj is the liquid flow rate outputtingstage j and inputting stage j þ 1, V j is the vapor flow rate outputting stage j and inputting stagej−1, Uj is the liquid side flow rate outputting stage j and W j is the vapor side flow rateoutputting stage j. The side streams U and W are used to represent the output streams likedistillate and bottoms, that is, D and B. These streams can occur as liquid (LB and LD ) or vapor(V B and V D ), in which D ¼ LD þ V D and B ¼ LB þ V B . We are going to consider n stages, withthe stage numbering starting on condenser (j ¼ 1) and continuing until reboiler is reached(j ¼ n). The generalization from Figure 2 to represent all stage is shown in Figure 3.

Considering the schematic representation of Figure 3, it is possible to consider side stream in

any stage, not only in the first but also in the last stages. A little care is needed in utilizingFigure 3 as a base for obtaining the mass and energy balances, that is, how there is no stage 0,so the streams U 0 and L0 that would output and stream V 1 that would input this stage do notexist; similarly, how there is no stage n þ 1, so streams V nþ1 and W nþ1 that would output andstream Ln that would input this stage do not exist. So, it is needed to fix W nþ1 ¼ V nþ1 ¼Ln ¼ U 0 ¼ L0 ¼ V 1 ¼ 0.So, one can obtain the mass balance in stage j as

Fj þ V jþ1 þ Lj−1 −V j −W j −Lj −Uj ¼ 0: (1)

The sum of mass balance in all stage gives us the global mass balance6 Distillation - Innovative Applications and Modeling

And the global mass balance of component i by

Or putting separated the bottoms and distillate

where xi j is the fraction of component i in the liquid phase of stage j, yi j is the fraction ofcomponent i in the vapor phase of stage j and zi j is the fraction of component i in the feedstream of stage j.

The energy balance in stage j, ignoring changes in kinetic and potential energies, is given by

where H Fj is the enthalpy of the feed stream to stage j, HVj is the enthalpy of the vapor streamfrom stage j and H Lj is the enthalpy of the liquid stream from stage j.8 Distillation - Innovative Applications and Modeling

Figure 3. Schematic representation of input and output streams in all stages of a distillation column.

Table 1. Four types of side streams.

10 Distillation - Innovative Applications and Modeling

Figure 4. Four types of side streams.

How V 1 ¼ 0, Eq. (12) is simplified to Eq. (10) by d1 ¼ 1=rD and how Ln ¼ 0, Eq. (12) is simpli- fied to Eq. (11) by dn ¼ 1=rB. Talking about side streams, there are four possibilities: no side stream, only liquid side stream, only vapor side stream and both liquid and vapor side stream. More details are shown in Table 1 and Figure 4.

4. Thermodynamics

Thermodynamics plays a key role on the modeling of phase equilibrium. For the phases of liquid and vapor in thermodynamic equilibrium, the fraction of component in each phase is connected by the iso-fugacity relation [15–19]

f Li ¼ f Vi (15)

where f Vi is the fugacity of component i in vapor phase and f Li is the fugacity of component i in liquid phase, which leads to the mathematical relation Steady‐State Modeling of Equilibrium Distillation 11 http://dx.doi.org/10.5772/66833

yi ¼ Ki xi (16)

where the way for calculating Ki depends on the chosen vapor liquid equilibrium (VLE)formulation, which can be Phi/Phi or Gamma/Phi [15–19], respectively,

^L φ Ki ¼ i (17) ^V φ i

γi φsat i Pi sat VL Ki ¼ exp ∫PPsat i dP (18) ^V φ i R T i

^ L is the fugacity coefficient of component i in liquid phase, φ

where φ ^ V is the fugacity coeffi- i icient of component i in vapor phase, φsat i is the fugacity coefficient of pure component i insaturation state, γi is the activity coefficient of component i in liquid phase, P is the pressure,Psat is the saturated vapor pressure, R is the ideal gas constant, V Li is the component i volume inliquid phase and T is the temperature.For the calculation of fugacity coefficient is required to use an equation of state (EOS) and forthe calculation of activity coefficient is required to use a model that represents the excess Gibbsfree energy. The saturated vapor pressure is calculated using one of the equation that describesthe relation between vapor pressure and temperature for pure components, like Antoine,Wagner, Riedel, Harlecher-Braun, among others [15–19]. These equations are based onClapeyron equation and their constant is obtained by experimental data fitting.

Another very important calculation that is needed to resort thermodynamics is the enthalpy.The liquid and vapor phases enthalpies are calculated [15–19], respectively, by

m H L ¼ ∑ xi HLi þ HE (19) i¼1

m H V ¼ ∑ yi H Vi þ HR (20) i¼1

where m is the number of components, H i is the enthalpy of pure component i, H E is the excessenthalpy that can be calculated by a model that represents the excess Gibbs free energy (EOS oractivity coefficient) and H R is the residual enthalpy calculated using an EOS.

For the calculation of pure component i enthalpy, it is necessary to specify a reference state.How we are considering that there is no reaction in the column and it is possible to put theenthalpies of all components equal to zero in a reference state (same conditions of temperature,pressure and phase). But, the intention here is to make the model as general as possible it willbe chosen elemental reference state that can be used also in a reactive system. In this referencestate (298K and 1 atm), the standard enthalpy of formation (ΔHf ), by convention, for an12 Distillation - Innovative Applications and Modeling

Figure 5. Calculation of the enthalpy of a component based on the elemental reference state. Steady‐State Modeling of Equilibrium Distillation 13 http://dx.doi.org/10.5772/66833

element in its most stable form standard state is zero [15–19]. The calculation of the enthalpy ofa component is based on the elemental reference state, shown in Figure 5.Where CP is the heat capacity at constant pressure of liquid (L) and ideal gas (IG), T bp is thebubble point temperature, T dp is the dew point temperature and ΔHVAP is the vaporizationenthalpy.

5. Materials and methods

In this section, will be presented the methods for generating the initial estimates and forsolution of equations showed above.

5.1. Initial estimates

The resolution of equations that models the steady-state equilibrium distillation columninvolves a set of highly nonlinear equation, mainly on phase equilibria and energy balances.The algorithms, for solution of this type of problem, request good initial estimates in order thatit can be possible to reach a solution. Moreover, here we are working in an algorithm thatavoids the use of methods for solving nonlinear equations systems, what makes the quality ofinitial estimate even more important.

There are a lot of methods for solving models of steady-state equilibrium distillation column,considering various levels of layout complexity, number of components involved and accuracyof properties calculation. Simpler models do not need initial estimates, but for more complexmodels, a good initial estimate is fundamental.McCabe-Thiele is a graphical method for combining the equilibrium curve with mass balance,assuming that there are two sections in the distillation column (between reboiler and feedstage and between feed stage and condenser) where molar vapor and liquid flow rates areconstant, in addition to the assumption that there is no heat loss, eliminates the need of energybalances [4], something like the non-heat effect presented below. Ponchon-Savarit is a graphi-cal method that includes energy balances, utilizing for this an enthalpy-concentration diagram[5, 6]. How, Ponchon-Savarit method utilizes energy balances and it is more accurate thanMcCabe-Thiele method. These methods do not need initial estimates but, unfortunately, areapplicable only for distillation of binary mixtures.

For complex systems, it is suggested that the procedure for solving this models should bebased on the solution of a system of nonlinear equations using an appropriated method forsolving systems of nonlinear equations like Newton-Raphson. This system of equations iscomposed by MESH equations or combinations of them. But, the solution convergence of thistype of problem is totally dependent on the quality of initial guess.

There are a lot of methods that use a technique called “tearing equations” that split large andsparse systems of algebraic equations into smaller system [20]. They are relatively simple, but arerestricted to ideal and nearly ideal mixtures. The methods of Lewis-Matheson [9], Thiele-Geddes14 Distillation - Innovative Applications and Modeling

[10] and theta [8] are based on equation tearing for solving simple distillation columns with one feed and two product stream. The bubble-point method receives this name because it tears the MESH equations in a way that a new set of stage temperatures is computed from bubble- point equations [11]. Similarly, the sum-rates method calculates, at each new iteration, the values of liquid streams by the summation of components flow rates in liquid phase [7]. The MESH equations wrote in this work will be rearranged for using tearing-equation method like bubble-point method, as can be seen in the next section. So, the idea here is to propose a method for generating good initial guesses aiming to avoid instability, normally presented for simpler method. That is, we are trying to join the efficiency of Newton-Raphson-like methods with the simplicity of methods based on tearing equations. It is already demonstrated that, with good initial guesses, it is possible to use tearing equation for very complex models like steady state for reactive distillation columns [13].

The algorithm at issue needs initial estimates for temperature, liquid and vapor streams and side streams. For initial estimates of temperature will be considered a model based on satura- tion temperature (T SAT ) of pure components at column operation pressure (Pcol ) and liquid, vapor and side streams will be estimated considering a non-heat effect.

For the initial estimates of stage temperatures (T ð0Þ ) will be considered a linear profile, in which, approximately in the middle of the column, we have an average temperature (T ave ) pondered on component fractions in feed streams m n ∑ T SAT i ∑ zi j Fj i¼1 j¼1 T ave ¼ n (21) ∑ Fj j¼1

For non-heat effects model is made the assumption of constant vaporization enthalpy, what can guarantee that the change in the liquid and vapor flow rates in each section of the column is due to only the feed quality, feed flow rate and side flow rates [21], as illustrated in Figure 6. Where the feed quality is defined as • Saturated liquid; Steady‐State Modeling of Equilibrium Distillation 15 http://dx.doi.org/10.5772/66833

At this point, we want to know just a rude value of side flow rates. So, let us make the rude assumption that feed and side streams are 50% in each phase and assume that the non-heat effects are valid. In this case, the expression

1 ðFj þ V jþ1 þ Lj−1 Þ (30) dj þ 1

is almost constant along the column. And, it can be used to generate initial estimates for side flow rates

With the initial estimates for side, liquid and vapor stream and temperature, it can be started the iterative process of steady-state model solution. The only unknowns lasting, to generate initial estimates, are the components fractions in each stream, but, in the algorithm, we are Steady‐State Modeling of Equilibrium Distillation 17 http://dx.doi.org/10.5772/66833

going to work; these initial estimates, showed how to generate, are sufficient for the calculationof components fractions. So, for these unknowns, it is not necessary to generate initial estimates.

5.2. Algorithm

When one talks about the solution of algebraic equation, it is necessary to keep in mind that forthe calculation of a number unknowns is necessary the same number of equations. In acomplex system of equations, it is not easy to be sure that we have the right number ofequations and unknowns. To make it easier to do, this balance is presented in Table 2.

Unknown type Number of unknowns Stage Equation(s) used to calculate

Temperatures n 1 to n The restriction that the sum of vapor mole fraction

• Feed flow rates, Fj for j ¼ 1, …, n;

• Feed temperature, T Feed

• Feed quality, qj for j ¼ 1, …, n;

• Feed fractions, zi j for j ¼ 1, …, n and i ¼ 1, …, m;

• Physical, critical and other properties of components, for evaluation of enthalpies and phase equilibrium. At this point, a more watchful reader must be thinking: it was used the restriction of vapor mole fraction sum, but was not used the same restriction for the liquid mole fraction, that is, right? Actually, this restriction is implicitly used, because the mass balance of a stage is the sum of mass balances by component in that stage and the sum of liquid mole fractions is forced to be equal to unity by a normalization step used in the algorithm presented ahead.

The sequence of calculation of the algorithm is presented in Figure 7.

Because the initial guess imprecision (mainly on temperatures) and the mole fractions of each component are calculated separately, especially in the first iterations, they may have values without any physical meaning (such as, negative or a sum different from unity,). So that, the convergence process of algorithm may be accelerated by normalization, undertaken by the following equation Steady‐State Modeling of Equilibrium Distillation 19 http://dx.doi.org/10.5772/66833

Figure 7. Algorithm for the simulation of steady-state distillation columns.

20 Distillation - Innovative Applications and Modeling

jxi j j xi j ¼ m (45) ∑ jxi j j i¼1

The temperatures are the only set of unknowns that cannot be calculated by a linear method. The temperatures are calculated stage by stage using the restriction that the sum of mole fractions in vapor phase must be equal to unit with aid of phase equilibrium relation, that is, m FðT j Þ ¼ 1− ∑ Ki j xi j ¼ 0 (46) i¼1

With the values of temperature and liquid mole fractions, it can be calculated the vapor mole fractions simply by using the phase equilibrium relation, that is, Eq. (38). The enthalpies of the all streams are calculated as previously shown. These enthalpies are used in the energy balances. The energy balances in stages 1 and n are used to calculate the heat duties on these stages. In the others stages, the heat transfer must be zero (adiabatic stages) or must be fixed in the input data.

QC ¼ Q1 ¼ F1 H F1 þ V 2 HV2 −W 1 H V1 −ðL1 þ U 1 Þ H L1 (48)

QR ¼ Qn ¼ Fn H Fn þ Ln−1 H Ln−1 −ðV n þ W n Þ HVn −Un HLn (49)

The value of vapor flow rate from stage n is obtained by using the mass balance in this stage

V n ¼ Fn þ Ln−1 −U n −W n (50)

And the values of vapor flow rate from stages 2, …, n−1 are calculated using energy balance with the aid of mass balances to eliminate the liquid flow rates terms. The calculation is made from n−1 back to 2

αj ¼ HVj −HLj−1 (54)

The energy balance normally is used to calculate the temperatures, but it would be necessary asolution of a system of highly nonlinear equations. Instead of this, the energy balances are usedto calculate the vapor flow rates, with aid of mass balances and some algebraic rearrangement,by sequential evaluations (one vapor flow rate at a time).The side flow rates are calculated by substituting the ratio between the side stream and thestream outputting a stage in the mass balance

dj Rj ¼ ðFj þ V jþ1 þ Lj−1 Þ (55) dj þ 1

W j ¼ ωj Rj (56)

U j ¼ ð1−ωj Þ Rj (57)

The liquid flow rates are calculated sequentially from stage 1 to stage n−1(remember, there isno Ln ) by using the mass balance in the respective stages

6. Results and discussion: case study

For the evaluation of the initial estimates and algorithm in question, it will be tested with anexample of hydrocarbons separation. Where a feed stream contains four hydrocarbons: pro-pane (C3), n-butane(n-C4), isopentane (i-C5) and n-pentane (n-C5). The operational conditionsare presented in Table 3.For representing the nonideal behavior of vapor phase, it was used Peng-Robinson equation ofstate, where were considered as mixing rule binary iteration parameters with geometric meanfor parameter a and arithmetic mean for parameter b. And for representing the liquid non-ideality, it was utilized UNIFAC method. The UNIFAC parameters, physical and criticalproperties for the components involved in the case of study, were taken from [16, 22], in whichphysical and critical properties are presented in Table 4.

Reboiler (stage 12) d12 ¼ 1=rB

ω12 ¼ ωB ¼ 0 B ¼ LB

Table 3. Operational conditions of distillation column.

B lnðPsat Þ ¼ A− (61) TþC

For a tolerance of 1 · 10−10 , it was needed 28 iterations to achieve convergence. A graphic of

error versus iteration is shown in Figure 8. In the start of the procedure, few steps present a high error reduction, after this a linear convergence rate is obtained. That is not as good as a quadratic convergence of an algorithm that uses a method for solution of nonlinear equations, like Newton-Raphson, but is justified by the simplicity of the solution algorithm. Figure 9 shows a comparison between initial guess and simulation results for stage tempera- tures. Initial guess profile is extremely close to results. Figure 10 shows comparisons between initial guess and simulation results for molar flow rates of the liquid and vapor phases. Initial guess of rates of both phases was extremely close to the values calculated by simulation. Steady‐State Modeling of Equilibrium Distillation 23 http://dx.doi.org/10.5772/66833

Table 5. Some simulation results.

26 Distillation - Innovative Applications and Modeling

The liquid mole fraction profiles calculated are shown in Figure 11. Some important numeric results of the simulation are shown in Table 5. In this case of study, the initial estimates generated are no more than 20% far from the final result, what confirm the goodness of the methodology used for generating the guesses. The results obtained here are very close to that obtained by King [23], some differences can be justified by different levels of accuracy of the thermodynamic modeling (the thermodynamic modeling of the cited reference is simpler). This case being studied aims to separate the propane from the other three hydrocarbons. For evaluating the influence of feed stage is presented in Figure 12, which presents the fraction of propane in distillate stream in function of the stage where the feed stream occurs. One can see in this figure that the best stage to put the feed stream is in the middle of the column. It is easy to understand, if the feed occurs near of condenser, there will be a great amount of components other than propane in the stages near of condenser, so part of it eventually outputs the column in the distillate stream and if the feed occurs near of reboiler, there will be a great amount of propane in the stages near of reboiler, so part of propane is present on bottoms stream.

The number of stage also has a great influence on the fraction of propane in distillate stream. It is obvious that, the more stages there are in the column, a greater mole fraction of propane there will be in distillate. But, it is possible to see in Figure 13 that after a certain number of stages, the increase on that fraction is too small. Figure 12 confirms what was verified in

Figure 12. Fraction of propane in distillate stream in function of feed stage.

Figure 13. Fraction of propane in distillate stream in function of the number of stages.

Figure 14. Fraction of propane in distillate stream in function of the reflux ratio.28 Distillation - Innovative Applications and Modeling

Figure 15. Heat load to reboiler in function of the reflux ratio.

Figure 13, because there is a comparison between column with the same number of stage, one with feed stream in stage six and another in the middle of column. And again the feed in the middle of column presents a better separation. Another parameter that has a strong influence on the mole fraction of propane in distillate stream is the reflux ratio, see Figure 14. Higher purity levels are achieved by increasing the reflux ratio, with a clear limit. But greater reflux ratio greater is the heat load to the reboiler, see Figure 15. After a certain value of reflux ratio, the increase in propane mole fraction is very small. With everything that has been exposed, one can see that achieving a better separation level is result mainly by spending more in operating or investment costs (greater reflux ratio, more stages, etc.) or changing the layout configuration of the operating system (feed stage location).

7. Conclusion

An algorithm was provided in this work for the solution of a distillation column operating in steady state; in this algorithm, the high nonlinear equations are solved in a very simple form. Equations in the model were divided into sets and each set was solved separately. The solution procedure uses an algorithm for solution of systems of tri-diagonal linear equation, explicit calculations and a method for root finding of equations of one unknown variable. A Steady‐State Modeling of Equilibrium Distillation 29 http://dx.doi.org/10.5772/66833

methodology was also provided to produce initial guess which constitutes a critical step in thesolution of nonlinear equations system. The modeling allows a variety of cases depending onthe types of condenser and reboiler, number and conditions of feed stream, side streams, etc.The suggested methodology for the production of initial estimates was efficient with valuesclose to those calculated by simulation. This fact accelerates and increases the convergencewarranty.

Author details

Vilmar Steffen1* and Edson Antonio da Silva2

*Address all correspondence to: vilmars@utfpr.edu.br

1 Academic Department of Chemical Engineering (DAENQ), Federal University of

Technology – Paraná (UTFPR), Francisco Beltrão, Brazil

2 Center for Engineering and Exact Sciences (CECE), State University of Western Paraná(Unioeste), Toledo, Brazil

Keywords: shortcut method, FUG, batch distillation

1. Introduction

Batch distillation is a process widely used for separation of small quantities of chemical com-pound of the one mixture as the recovery of small quantities of hazardous materials in wastestreams, recovery of solvents, as well as, for pharmaceutical and biotechnological productswith high added value, among others. Therefore, the development of mathematical modelsfor the prediction of a process has a high interest in recent times [1–4].

Batch distillation is a flexible process because one equipment can obtain the separation of allthe components of the mixture, while the continuous process [5] requires a number of col-umns distillation equal to the number of components minus one (n − 1). Another advantage32 Distillation - Innovative Applications and Modeling

of batch distillation process is the use of the same equipment for the mixture separation with different compositions or different mixtures [6]. On the other hand, the disadvantage of the batch distillation with respect to continuous distil- lation is that only small amounts of products can be obtained of the mixture. Another disad- vantage is the production of waste unwanted for each cuts, however, these residual cuts can be separated into the same column [7].

A batch distillation column can be operated using any of the following policies [1]:

(1) Constant reflux.

(2) Variable reflux.

(3) Optimal reflux.

(4) Reflux profile.

The process behavior can be predicted by developing mathematical models based on mass and energy balances. The mathematical models obtained can be classified as [1, 8, 9]:

(1) Simplified (shortcut method).

(2) Semirigorous.

(3) Rigorous.

(4) Order reduction.

Currently the rigorous models have an area of great interest and these require especially the use of computers with high accuracy and processing capabilities; however, simplified methods can be applied with the use of the equipment such as tablets, smart phones, and/or laptops with smaller capacity of data processing, which makes possible the search for predict- ing the behavior of the process [2, 10]. In addition, the use of this kind of methods is a tool for obtaining initial data for the mathematical optimization.

Unlike the rigorous methods that considered the dynamics of the complete column, the short- cut methods are mathematical models that predict the behavior of the process considering the least amount of equations, usually making an overall material balance and partial balances considering a component any “i.” The main limiting factor of these shortcut methods is to find a functional relationship between the concentrations of the dome and the bottom.

The shortcut methods are justified because these require a minor calculus time and memory requirements, as well as, an acceptable accuracy in the results obtained with respect to the rigor- ous method. These are an appropriate tool to obtain initial values for the mathematical optimiza- tion of some process, when the complexity of the methods required data very close to the solution.

The shortcut method is also used for the columns design and obtaining of limit conditions as minimum reflux ratio, Rmin and minimum number of stage Nmin. On the other hand, the short- cut methods are very simple to apply and to program, therefore, are useful in the teaching- learning process. Short-Cut Methods for Multicomponent Batch Distillation 33 http://dx.doi.org/10.5772/66830

The two most important shortcut methods reported in the literature made use of the Fenske-Underwood-Gilliland (FUG) method developed for continuous distillation, but consideringthat the feed changes at every instant; that is, the bottom product in the current time is thefeed for the next time (step).The first of the shortcut methods was developed by Diwekar [11] and reported in the litera-ture by Diwekar and Madhavan [12]. This method was developed considering the policiesof constant and variable reflux. This method used the Hengstebeck-Geddes equation. Thismethod also performs the comparison between the values of the minimum reflux ratio ofUnderwood and minimum reflux ratio of Gilliland, which increases the computational timebecause it uses an additional iterative process.

The second method was reported by Sundaram and Evans [13] and only considered the con-stant reflux policy and the Fenske Equation. The model obtains a solution in two parts; anouter loop that solves material balances and internal one that solves the functional relation-ship between the compositions of the dome and the bottom using the FUG method. The math-ematical model developed initially considered:

(1) Constant relative volatilities.

(2) Constant molar flow.

(3) Negligible vapor and liquid accumulation in trays and the condenser.Based on the work of Sundaram and Evans [13], Narváez-García et al. [10] developed a math-ematical model for batch distillation process using a variable reflux policy.

The present studies show the most important shortcut methods used to predict the behaviorof the batch distillation process.

2. Important definitions

For the use of the Underwood equations, this work considered separations Class I and ClassII. In according to Shiras et al. [14] defined Class I and Class II as follows: Class I: “Separations such that, with infinite plates, all components of the feed are present in both the top product and bottom product.” Class II: “Separations such that, with infinite plates, some of the components are completely in the top product or completely in the bottom product.”Similarly, an important concept in model developments is the key component light (lk) andheavy key component (hk) defined as follows: Light key component (lk): Light component that is present in the residue in impor- tant amounts. Heavy key component (hk): Heavy component that is present in the distillate in important amounts.34 Distillation - Innovative Applications and Modeling

3. Reflux policies

When a fraction of the product obtained is fed back into the process and this can be done on four operations of the process: (1) constant reflux, (2) variable reflux, (3) optimum reflux, and (4) profile of reflux. In either case, the reflux ratio (R) is defined as L R = ​___ ​ ___ dD ​ D​L​(​t ​) ​​ = ​__ = ​____ L D ​​ (1) ​ dt ​

where L is the reflux in the dome and D the product flow.

For some type of reflux used, it should be considered if there is accumulation of liquid and vapor in each of the trays as well as in the reflux tank. Another aspect that should be consid- ered is where the initial feed is introduced because when it is performed from the reflux tank, the accumulation in each of the stages is equal to feed initial concentration, if conversely, the feed is introduced in the reboiler and column is operated without reflux, the concentration of each of the trays is equal to the concentration of the vapor phase and will be in equilibrium with the feed [15]. Constant reflux: In constant reflux policy, the product concentration varies with time because new feed input does not exist, so that the initial mole fractions of the more volatile are depleted and the molar fraction of the final distillate is an average. Variable reflux: The batch distillation process with a variable reflux policy is used when it is desired to obtain a constant product concentration. In others words, reflux ratio is modified such that at each instant the same concentration of distillate is obtained. Optimal reflux: For optimum reflux policy, the process used an objective function directly related to a control variable, which usually is the reflux ratio. This function is solved by apply- ing mathematical methods such as dynamic programming, variation calculation, pontryagin maximum principle or nonlinear programming (NLP), among others. In general, the process is considered as an optimal control problem and the most common cases studied in the lit- erature are [16]: (a) maximum distillate problem, (b) minimum time problem, (c) maximum profit problem, (d) minimum energy problem, and (e) maximum thermodynamic efficiency problem.

Reflux profile: For this case, a combination of constant reflux and variable reflux are used for obtaining a given concentration of the desired product in a time given. This operation policy is a derivation of the optimization process.

4. Materials and methods

In this work is considered a batch distillation column with the following characteristics:

The mathematical model of the column is obtained by performing a total mass balance andpartial mass balances to component “i.” The Fenske-Underwood-Gilliland method is used tofind the functional relationship between the compositions of the bottom and the dome of thecolumn.

Although it presents the development of the model, considering the policies of operation ofconstant and variable reflux, these are presented in only four cases of study for the shortcutmethod to reflux variable considering the contribution to the state of the art of the authors.

In each case, it is considered that the mixture is fed to the boiling temperature. The errortolerance is 10−4, the integration step is Δt = 10−1 h and the time of production is required todeplete the lighter component. It has been considered a feed of 200 kmol and a vapor flow of110 kmol h−1. For these cases, it is considered that the relative volatility is constant throughoutthe process.

The value of the vapor flow was established so that it allows to deplete the most volatilecomponent in a small operation time. For the ternary and quaternary mixtures only first cutis considered. For validation, the results of both methods, Diwekar [11] and Narváez-Garcíaet al. [10], are compared with the results using the rigorous method presented by Domenechand Enjalbert [17]. This model is used because it is considered as a low holdup. To solve eachone of the cases was made a program in Fortran language.

5. Simplified mathematical models

The complete mathematical model of a batch distillation column considering the dynamics ofthe process consists of a system of differential equations and algebra (DAEs) added by equa-tions that allow the calculation of the thermodynamic properties and hydraulic conditionsof the column. The solution of the system can be very complex depending on the state equa-tions used to predict the behavior of the gas phase (Soave, Redlich-Kwong Peng-Robinson,etc.) or the solution of the models used to predict the liquid phase behavior (Wilson, NRTL,UNIQUAC, UNIFAC, etc.).

According to Diwekar [9], the number of equations in a rigorous mathematical model of a

of equations consider the total restrictions in each of the stages (​​∑​ ​​ x = ​∑​ ​​ y = 1​), the expression of reflux ratio (R = L / D), and liquid (L) and vapor (V) flows calculations along the column. The number of equations increases if the calculation of other variables of interest such as the column hydraulic or thermodynamic efficiency is considered.

The solution of this equation system is complex and requires intensive use of computers with adequate processing capacity, which affects costs in the area of process simulation. Therefore, it is needed to consider some simplifications to the mathematical model to reduce the data processing time.

Reductions to the batch distillation mathematical model are possible if it is considered that the process is continuous, with a feed that changes in every moment as shown in Figure 1 [1, 10], which allows to use equations Fenske [18], Underwood [19], and Gilliland [20] of continuous distillation (FUG method).

Figure 1. Scheme of a batch distillation column for the shortcut method.

Gilliland correlation can be replaced by the correlation Eduljee [21] because the mathematical expression is simpler for numerical works. The shortcut method considers:

(1) Constant molar flow along the column.

(2) Constant relative volatilities throughout the process.

(3) Negligible fluid and vapor accumulation within the column.

Constant molar flow is based on the assumption that the enthalpy of vaporization is the same for all components, which is correct if the mixture consists of very similar compounds. Short-Cut Methods for Multicomponent Batch Distillation 37 http://dx.doi.org/10.5772/66830

The simplification is more restrictive from shortcut method to consider constant relative vola-tilities throughout the process. This consideration significantly reduces the number of calcula-tions in the model, especially because the iterative processes of liquid-vapor equilibrium doesnot apply. When the relative volatility cannot be considered as a constant amount along thetime or the column, polynomial expressions or Winn [22] equation can be used to estimatethe changes; therefore, Diwekar [11] suggested that the relative volatilities can be used tocalculate in every moment of the process using an average between the values of the bottomand the dome.

Finally, the vapor accumulation in a distillation column can be neglected because it is muchless than the cumulative amount of liquid, and the accumulation of fluid in the column canbe neglected, considering that this accumulation is less than the liquid accumulated in thereboiler. Under these circumstances, the two most important shortcut methods for batchdistillation in the literature were reported by Diwekar [11], Sundaram and Evans [13], andNarvaez-García et al. [17].

5.1. Shortcut methods derived from FUG method

5.1.1. Shortcut method developed by Diwekar [11]

The first shortcut method for batch distillation presented here was developed by Diwekar[11]. This method considers a global balance in the column and their respective partial bal-ances (component “i”); each of the equations used in the method are presented below:Global balance: ​ dB ___ ​ dt ​ = − D; ​B0​ ​ = F​ (2)

where D is the distillate obtained by a mass balance in the dome of the column: V D = ​____ ​ R + 1 ​​ (3)

In the variable reflux case, Diwekar [11] uses a function obtained from the equationHengestebeck-Geddes (Eq. (21)), considering the sum of all components, and applying thesum in both members of this equation is obtained:

(a) The concentration of component reference (k) in the dome (Eq. (32)) is calculated. (b) Other concentrations are calculated using the Hengestebeck-Geddes equation (Eq. (22)). (c) Increase the time (∆t). (d) New concentrations (Eq. (20)) and the remaining amount in the reboiler (Eq. (18)) are calculated.40 Distillation - Innovative Applications and Modeling

(2) To propose an initial value of C1, which will be adjusted by an iterative process.

(3) To calculate the reference component concentration in the dome (Eq. (32)).

(4) Other concentrations are calculated using Equation Hengestebeck-Geddes (Eq. (21)).

(5) To solve Underwood equations (22) and (23).

(6) To solve Gilliland equation.

(a) First Eq. (24).

(b) Second Eq. (26).

(c) Finally, Eq. (27).

(7) Verify that the obtained value by Underwood equations is the same to that obtained by Equation Gilliland.

(a) To use Eq. (31).

(b) If this is not true it is necessary to change the value of C1 with some iterative process as the Newton-Raphson method.

(c) The process is repeated from step 2 to achieve convergence.

(d) If this is true go to step 8.

(8) Increase the time (∆t).

(9) Calculate new concentrations (Eq. (20)) and the remaining amount in the reboiler (Eq. (18)).

(10) The process is repeated until the desired time production.

Variable reflux policy.

(a) Consider constant the concentration of reference component (k) in the dome.

(b) Other concentrations are calculated using the equation Hengestebeck-Geddes equa- tions (Eq. (21)).

(c) Increase the time (∆t).

(d) New concentrations (Eq. (20)) and the remaining amount in the reboiler (Eq. (18)) are calculated.

(2) To propose an initial value of C1, which will be adjusted by an iterative process.

(3) Verify that Eq. (31) is zero.

(a) If this is not true it is necessary to change the value of C1 with some iterative process as the Newton-Raphson method until converge. Short-Cut Methods for Multicomponent Batch Distillation 41 http://dx.doi.org/10.5772/66830

(4) Other concentrations are calculated using Equation Hengestebeck-Geddes (Eq. (21)).

(5) To solve Underwood equations (22) and (23).

(6) To solve Gilliland equation.

(a) First Eq. (27).

(b) Second Eq. (24).

(7) Calculate the value of the reflux ratio R with Eq. (26).

(8) Increase the time (∆t).

(9) Calculate new concentrations (Eq. (20)) and the remaining amount in the reboiler (Eq. (18)).

(10) The process is repeated until the desired time production.

5.1.2. Shortcut method developed by Sundaram and Evans [13] using a constant reflux policy

In the method of Sundaram and Evans [13], the total material balance (Eq. (2)) and partial (Eq.(4)) are similar to the method of Diwekar [11], and Eqs. (18) and (20) are the same; however,Eq. (20) may be a function of the remaining liquid in the bottom; therefore, Eq. (6) calculatesthe change in the mole fractions in the bottom, then: ​ dB d ​xB​ (i)​ ​ = [ ​xD​ (i)​ ​ − ​xB​ (i)​ ​ ] ___ ​ B ​ ​ (33)

Considering very small changes in the above equation; therefore, it is obtained:

________ (​B​ ​ − ​B​ ​ ) Δ ​x​ (k)​ ​

Substituting Eq. (37) into Eq. (35), Eq. (20) is obtained. Eq. (28) is easily solved; however, Eq.(30) and Eq. (35) are much more complex because they require the functional relationshipbetween the concentrations of the bottom and the dome.

The functional relationship between the concentrations of the dome and the bottom is calcu-lated using the Fenske equation considering the minimum number of separation stages (Nmin)with the mole fractions of the dome (xD) and bottom (xB):

​ − 1 In this method, it is also necessary to consider the composition of a component (k) of reference; then, using the Fenske equation, the composition of the reference component is isolated. Therefore, it is necessary to considerer the sum of all components. From Eq. (35), the following is obtained:

(5) Back to step 2 until achieve the desired production time.

5.1.3. Short method developed by Narváez-García et al. [10] using a variable reflux policy

This proposal is based on the concepts of Sundaram and Evans [13]. It is initiated by calculat-ing the reflux ratio required to obtain the desired product; therefore, using Eq. (26) and solv-ing it, the following is obtained: X + ​R​ ​ R = ​______ ​ 1 − Xmin ​​ (43)

Eq. (48) requires the Nmin value, therefore, it is necessary to obtain Nmin for the shortcutmethod. In this sense the Fenske equation allows to calculate the minimum number of trayswhen the light key component (lk) and the heavy key component (hk = k) are considered,then:

With the Nmin value, the reflux ratio and other values relating to the variable Nmin can be calcu- lated. The proposed solution to the developed method is addressed in the following section. It is notable that both the model of Diwekar [11] and this model started from the same mate- rial balances (global and partial), and in other words, both works are developed following the same method; however, the functional relationship between the concentrations of the dome and bottom is different equations. Table 1 presents a comparison between the equations of the two models.

In fact the equations of Underwood and Gilliland are the same in each model, and the differ- ence is the way of how the values of the Nmin are obtained. Narváez-García et al. [10] used the Fenske equation, while Diwekar [11] used the equation of Hengestebeck-Geddes.

While calculation times are similar in both models, the Narváez-García et al. model has an advantage over the Diwekar model when the separation of mixtures Class I is performed due to the use of a simplified Underwood equation (Eq. (39)). This does not happen with the model of Diwekar because the original equations of Underwood are always considered. Short-Cut Methods for Multicomponent Batch Distillation 45 http://dx.doi.org/10.5772/66830

5.1.3.1. Solution algorithm (Narváez-García et al. [1])

The mathematical model by Narváez-García et al. [10] is conformed for the system of Eqs. (22)and (23) or (39), (35), (37), (43), (48), (49), (54), (55), (57), (58), and (59). The main objective ofthis system of equations is to calculate the value of the reflux ratio and for this Eq. (40) is used.

Eq. (43) requires the value of X and Rmin. The value of X is related to the minimum numberof trays (Nmin) through Eqs. (48) and (49); therefore, first Nmin is calculated, starting with anassumed value and is iterated until it converges to the correct value of Nmin.

The Newton-Raphson iterative method used Eqs. (57)–(59). These equations are only functionof the dome and bottom concentrations of as well as of the relative volatilities.46 Distillation - Innovative Applications and Modeling

The value obtained of X allows to find the value of Rmin, which is solve using the Underwood equation (39). However, to get the value of Rmin before it is necessary to calculate the mole frac- tions of the dome (xD) using Eqs. (40) and (54). With the values of X and Rmin will be calculated the reflux ratio R (Eq. (43)) and now it is possible to calculate the amount remaining in the reboiler using Eq. (37) and the bottom concentration using Eq. (35).

6. Cases of study

The mathematical models of the shortcut method presented in this work have been solved considering various mixtures: binary, ternary, and quaternary. Being the variable reflux pol- icy more complicated than the constant reflux policy, only are presented cases considering the variable reflux policy. The input conditions to the process are shown in Table 2.

Case Feed molar fraction Relatives volatilities (α) N+ k ​(​lk​)​

​x​ ​ ​ D

1 2 3 4 1 2 3 4

1 0.40 0.20 0.30 0.10 1.67 1.25 1.00 0.83 5 3 0.70

2 0.33 0.33 0.34 – 1.33 1.00 0.67 – 10 2 0.80

3 0.50 0.50 – – 2.40 1.00 – – 9 2 0.95

N = Number of trays, k= Reference, Component = 1, 2, 3, 4.

+

Table 2. Input conditions for cases of study.

7. Results and discussion

The results of the cases of the study are shown below. Considering that, the mole fraction of the desired component is a constant amount, the profiles of the reflux ratios, the remaining amounts in the bottom and its concentrations are obtained. To validate the results of the reflux rate obtained by the shortcut methods, a comparison between the profile of the reflux ratio obtained and the profile obtained with a rigorous method was performed.

7.1. Case 1

Figures 2, 4, and 5 show the results obtained with the short methods of Diwekar [11] and Narváez-García et al. [10]. Figure 3 shows the result comparison between the shortcut method and the rigorous method. The comparison of the results between the two shortcut methods (Figures 2, 4, and 5) allows to establish that there are no significant differences. The maximum deviation for reflux was 1.5%, the amount remaining in the reboiler was 0.55 %, and concentrations in the bottom was 2%. Short-Cut Methods for Multicomponent Batch Distillation 47 http://dx.doi.org/10.5772/66830

Figure 2. Reflux ratio profiles obtained with the shortcut methods.

Figure 3. Comparison of profiles of reflux ratio using the shortcut method and a rigorous method.48 Distillation - Innovative Applications and Modeling

As for the comparison between the shortcut method and the rigorous method (Figure 3), thedeviations are within an acceptable range of 9.7% maximum considering the reflux ratio iscalculated.

7.2. Case 2

Figures 6, 8, and 9 show the results obtained with the short methods of Diwekar [11] andNarváez-García et al. [10]. Figure 3 shows the results comparison between the shortcutmethod and the rigorous method.

Figure 6. Reflux ratio profiles obtained by shortcut methods.

The results between both short methods (Figures 6, 8, and 9) allow to establish that there areno significant differences. The maximum deviation for calculated reflux ratio was 2.2%, forthe amount remaining in the reboiler was 0.29%, and the deviation in the bottom concen-trations was 0.67%. As for the comparison between the shortcut method and the rigorousmethod (Figure 7), the deviations are within an acceptable range of 9.7% maximum consider-ing the reflux ratio is calculated.50 Distillation - Innovative Applications and Modeling

Figure 7. Comparison of profiles of reflux ratio obtained using the shortcut method and a rigorous method.

Figures 10, 12, and 13 show the results obtained with the short methods of Diwekar [11]and Narváez-García et al. [10]. Figure 11 shows the results comparison between the shortcutmethod and the rigorous method.

Figure 10. Reflux ratio profiles obtained by shortcut methods.

52 Distillation - Innovative Applications and Modeling

Figure 11. Comparison of profiles of reflux ratio obtained using the shortcut method and a rigorous method.

The results between both short methods (Figures 10, 12, and 13) allow to establish that thereare no significant differences. The maximum deviation for calculated reflux ratio was 2.7%,the amount remaining in the reboiler was 0.45%, and the deviation in the bottom concen-trations was 0.63%. As for the comparison between the shortcut method and the rigorousmethod (Figure 11), the deviations are within an acceptable range of 3.8% maximum consid-ering the reflux ratio is calculated.

In general, as shown in each of the figures, the maximum deviation found between the twoshortcut methods considering a policy of variable reflux is less than 3% and, in this sense, theuse of either of the two depends on the ease of application of the method.

In this case, the method developed by Narváez-García et al. [10] is better because it is adjustedto the original equations of the FUG method.

Similarly, to validate the shortcut methods considering a variable reflux policy, we hadpresented a comparison between the profiles of the reflux ratio which shows that you canhave up to 9.7% difference between the results of the shortcut method and the rigorousmethod, of course, this difference is due to the simplifications of the short method, how-ever, the difference falls within an acceptable range and this validated the shortcut meth-ods presented. The maximum difference found between the concentrations of the bottomwas less than 2%.

In all cases, the behavior of the profiles is adequate for the batch distillation process; in otherwords, greater process time is necessary for a greater reflux and the more volatile componentis depleted.54 Distillation - Innovative Applications and Modeling

8. Conclusions

In this chapter, we have presented the shortcut methods developed by Diwekar [11], Sund- aram and Evans [13], and Narváez-García et al. [10]. Considering the complexity of the solution only, the shortcut method with a variable reflux policy is solved. The results were validated using a rigorous method. It is considered that the results of the shortcut methods are very close with respect to the rigorous method results.

Mathematical Modelling of Batch Distillation Columns:

Adriana del Carmen Téllez-Anguiano,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66760s

Abstract Distillation is the process most commonly used in industry to separate chemical mix- tures; its applications range from cosmetic and pharmaceutical to petrochemical indus- tries. The equipment required to perform the distillation process is known as distillation column. Since initial investment and maintenance costs for distillation columns are very high it is necessary to have an appropriate mathematical model that allows improving the comprehension of the column dynamics, especially its thermal behaviour, in order to enhance the control and safety of the process. This chapter presents a general panorama of the mathematical modelling of distillation columns, having as a specific case of study the comparison of a space-state non-linear model and a Takagi-Sugeno fuzzy model for a batch distillation column using a binary mixture (Ethanol-Water).

Distillation is the process most commonly used in industry to separate chemical mixtures,being the petrochemical industry one of the most important due to that oil distillation allowsobtaining useful product, such as fuels. Distillation is also widely used in the pharmaceuticaland cosmetics industry in order to obtain specific drugs and in the liquor industry to obtainwines and liquors, among other applications [1].58 Distillation - Innovative Applications and Modeling

Distillation columns are the essential equipment required to perform the distillation process, these columns allow producing food, fuel, medicine, among other products. However, distil- lation columns represent an important investment in the process they are used, that is why it is necessary to have both, corrective and predictive maintenance, in order to prevent failures in the process as well as in the equipment.

Through the computational and technological continuous development, the industrial pro- cesses, such as distillation, have become very complex systems due to the high number of components they have and the several functions they develop, so their vulnerability has also increased. Having appropriate techniques to model distillation columns, such that these models allow implementing efficient and reliable control techniques, is very important to obtain the desired product quality, the adequate process functioning and to improve the security of the system and the user.

In the literature, different mathematical models have been used to improve distillation col- umns dynamics and comprehensions have been reported. Simple linear and non-linear models are representations that consider only few variables and low-order equations, simplifying the design and implementation of controllers using computational tools. Kienle [2] presents a low- order model for an ideal multicomponent distillation process considering the non-linear wave propagation theory.

Balasubramhanya and Doyle Iii [3] present a low-order model for a reactive multicomponent distillation column as well as the designing of a (MPC) predictive control to obtain the best quality of the distilled product. In Ref. [4], a model based on neural networks having the aim of optimiz- ing the energy efficiency in a binary distillation column is presented. Lopez-Saucedo et al. [5] present the simulation and optimization of a model for a conventional and nonconventional batch distillation column.

Astorga et al. [6] and Cervantes et al. [7] present high-gain observers to estimate the light component composition in a continuous distillation column using a set of models for each plate of the column. In Ref. [8], a fault tolerant scheme for a distillation column, where observers are used to detect failures in the temperature sensors considering a non-linear model of the distillation column, is presented. The parametric identification is other methodology used to estimate certain variables in distillation columns as presented in Refs. [9, 10].

The Takagi-Sugeno fuzzy model is a useful tool to model and control complex systems based on the concept of decomposing a non-linear model in a multi-model structure formed by linear models not necessarily independents and fuzzy logic [11, 12], where the non- linear system representation is obtained through a weighted sum of all the sub-systems. The Takagi-Sugeno fuzzy model provides a solution to solve the designing and implemen- tation issues in control strategies for non-linear systems, for instance, Wang et al. [13] propose a methodology to design control techniques for systems having a Takagi-Sugeno form.

The stability analysis of the Takagi-Sugeno fuzzy model can be solved considering the Lyapunov approach and by using the inner point tool as well as optimization techniques based on linear matrix inequalities (LMIs) [14]. Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 59 http://dx.doi.org/10.5772/66760s

In this chapter, the design and simulation of a non-linear state-space and Takagi-Sugeno modelsfor a batch distillation column are presented. These models are simulated and compared in orderto analyse if they aim the objective of representing adequately the process dynamics in order tofacilitate the implementation of control strategies to improve the distilled product quality as wellas the process security.

2. Distillation column operation modes

Due to the variety of substances found in the nature and their different phases (mainly liquidand vapour), there exist different distillation operation modes in order to separate diversemixtures, obtaining different quality of products.The main distillation operation types are as follows:• Vacuum distillation: A low-pressure system is used in order to obtain a low-temperature boiling of the substances in the mixture. Usually, a vacuum pump is used to generate the low-pressure state, as shown in Figure 1a.• Destructive distillation: The substance is heated at high temperatures to be decomposed in other products that can be separated by fractionating, its operation is similar to the one used in wood and coal, as shown Figure 1b.• Extractive distillation: Different separation agents are added to azeotropic mixtures, alter- ing the relative volatility of the mixture components in order to allow their separation (see Figure 1c).• Fractionating distillation: Liquid mixtures are separated by heating, considering a high heat exchange and the liquid and vapour molar rates. This distillation is used to separate composite mixtures/substances having different but close boiling temperatures. It usually considers a continuous operation, having a constant feeding flow through a feeding tray. The section above the feeding tray is named rectifying section, under the feeding tray is called stripping section, as shown in Figure 2a.• Batch distillation: Widely used in industry when having small liquid quantities or when obtaining different products from a single mixture load is required. This operation does not have steady state due that the mixture composition varies in time; besides, it only allows enriching or rectifying the distilled (lighter) product (see Figure 2b).In general, the different distillation operation modes have the same operating principle, mainlydue the physical variables that interact in the process, such as temperature, composition,pressure and heating energy.A typical distillation column is formed by a boiler, a condenser and n trays. The boiler is theelement that provides the heating energy necessary to evaporate the mixture into it. Thecondenser provides the cooling necessary to condensate vapour, part of this vapour returns tothe column to enrich the mixture, the rest is obtained as a distilled product. The column bodyis composed of a set of trays, where a partial separation of the mixture is performed due thecirculation of liquid and vapour flow.60 Distillation - Innovative Applications and Modeling

The vapour flow is generated by the ebullition of the mixture in the boiler, the vapour rises into the column body and it is enriched by the light element of the mixture in each tray of the column. The liquid flow, generated by the reflux, descends from the condenser to the boiler by gravity and it is enriched by the heavy element of the mixture in every tray of the column. This operation can be described by an adequate mathematical model of the process. Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 61 http://dx.doi.org/10.5772/66760s

3. Distillation column mathematical modelling

The main objectives of designing a mathematical model of the distillation process are tosimplify the analysis and comprehension of the distillation dynamics, facilitate the design ofcontrol techniques to enhance the distilled product quality and the system performance,estimate variables difficult to be measured, diagnose failures, among others. In order to dealwith these objectives development of an adequate model is indispensable.

There exist different distillation column models according to its operation, the most commonlyused in industrial applications are the continuous (fractionating) and batch models. Because ofthe similarity between the continuous and the batch operating types, in this section, a genericmodel that presents adequate results in both cases is presented.

It is well known that having a more complete/complex model implies having more complexequations difficult to solve, whereas having a simpler representation implies having simplerequations but the response resolution will have a higher calculation error compared to the realsystem response.

In general, there are two main model types according their complexity: simple and complex.The simple model found in the literature is the differential model, which considers the boilerand the condenser as trays in the distillation column. The column dynamics is represented bythe component mass balance as shown in Eq. (1).

dWxw Wdxw xw dW ¼ þ ¼ −DyD (1) dt dt dt

where W is the bottom product, xW is the bottom product composition, D is the distilledproduct and yD is the distilled product composition.

The complex model considers each column element individually, i.e. a condenser, a boiler andtrays are modelled individually, such that the response has a better resolution.

The particular study case presented in this chapter considers a complex model of a batchdistillation column using a binary mixture.

4. Non-linear model of a binary batch distillation column

The model for a binary batch distillation column is obtained considering the light component,this component is obtained as a final (distilled) product [15]. The light component compositionis obtained in each tray of the distillation column, where the liquid and vapour molar flowsinteract.

In order to design the distillation column model, the following assumptions are considered[16]: total condenser, no heating losses in the body column, constant pressure in the bodycolumn, liquid and vapour phases in thermodynamic equilibrium in each plate, variablerelativity volatility according to the component composition.62 Distillation - Innovative Applications and Modeling

The distillation column dynamics is represented by a set of differential equations that describe the behaviour of the light component of the mixture, given by Eq. (2).

dxi Lðxi−1 −xi Þ þ Vðyiþ1 − yi Þ

¼ (2) dt Mi

where xi is the liquid molar composition of the light component in tray i, yi is the vapour molar composition of the light component in tray i, L is the liquid molar flow, V is the vapour molar flow and M is the retained mass. The phase equilibrium is determined by constant K, as shown in Eq. (3) for ideal mixtures.

xi K¼ (3) yi

Such that considering the vapour-liquid equilibrium (VLE) and the relative volatility, the vapour composition as a function of the liquid composition is obtained. This function is presented in Eq. (4).

y ¼ f ðx, αÞ (4)

This is specifically presented in Eq. (5).

αi xi yi ¼ (5) 1 þ ðαi −1Þxi

where α is the relative volatility in tray i.

Within each element of the distillation column flow different molar rates/quantities, named molar flows. These flows are the liquid and the vapour entering and leaving each tray, the distilled product and the bottom product. In a binary batch distillation column, the liquid flows in both rectifying and stripping sections are the same, as well as the vapour flows, because there is not feeding flow.

L ¼ LS ¼ LR (6) V ¼ VS ¼ VR

The molar flows considered in the binary batch distillation model are four: vapour (V), liquid (L), distilled (D) and bottom (B) products, these are expressed in Eqs. (7)–(9) [17].

QB V¼ vap vap (7) H1 xn þ H1 ð1−xn Þ

where QB is the heating power (input), xn is the liquid composition of light component in the vap vap boiler (tray n), H1 is the vaporization enthalpy of the light component and H 2 is the vaporization enthalpy of the heavy component. Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 63 http://dx.doi.org/10.5772/66760s

L ¼ ð1−RÞV (8)

where R is the reflux input.

D ¼ V−L (9)

B, the bottom product, is not calculated, it is considered as the molar flow that remains into theboiler.

The non-linear model of the binary batch distillation column presented in this chapter is basedon a set of sub-models, each sub-model corresponding to a specific element of the column(boiler, condenser and trays).

4.1. Condenser sub-model

The condenser is numbered as tray 1. Its dynamics is described by Eq. (10).

dx1 Vy2 −Lx1 −Dx1

¼ (10) dt M1

By substituting L ¼ ð1−RÞV in D ¼ V−L, in order to represent the condenser as a function of the

reflux, Eq. (11) is obtained.

D ¼ RV (11)

By substituting Eq. (11) in Eq. (10), Eq. (12) is obtained.

dx1 Vy2 −Lx1 −RVx1

¼ (12) dt M1

Considering that α2 x2 y2 ¼ (13) 1−ðα2 −1Þx2

the non-linear equation that represents the condenser dynamics is finally represented inEq. (14).

dx1 V α2 x2 Lx1 RVx1 ¼ − − (14) dt M1 1−ðα2 −1Þx2 M1 M1

4.2. Tray sub-model

The column body is formed by a set of n-2 trays. Eq. (15) describes its dynamics.

dxi Vyiþ2 −Vyi þ Lxi−1 −Lxi

¼ ; i ¼ 2, 3, …, n−1 (15) dt Mi

where n is the total number of trays including a boiler and a condenser.

64 Distillation - Innovative Applications and Modeling

Considering that αi xi yi ¼ (16) 1−ðαi −1Þxi

the non-linear equation that represents the condenser dynamics is finally represented in Eq. (17).

In this section, the distillation column sub-models shown in Eqs. (14), (17) and (22) are presented in a state-space representation having the form shown in Eq. (23). x_ ¼ Ax þ Bu (23)

This representation is used in a specific study case, a 12-tray distillation column including a boiler and a condenser, using a binary mixture in a batch operation. Compositions Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 65 http://dx.doi.org/10.5772/66760s

5. Takagi-Sugeno fuzzy model for a binary batch distillation column

The Takagi-Sugeno fuzzy representation describes the system dynamics based on linear sub-models interpolation and fuzzy rules [18].

Rule for model j:

If z1 ðtÞ is M1j j, z2 ðtÞ is M2j ,… and zp ðtÞ is Mpj

Then: r xðtÞ ¼ ∑ Aj xðtÞ þ Bj uðtÞ (26) j¼1

where j = 1, 2,…, r, Mj is the fuzzy set, r is the sub-model number, x is the state vector, u is theinput vector, Aj is the state matrix for sub-model j, Bj is the input matrix for sub-model j andzj ðtÞ is the scheduling measurable variable (state variables or external disturbances).

Given ½xðt, Þ, uðtÞ, zðtÞ, the complete fuzzy model is obtained by using a singleton-typefuzzifier, a product-type defuzzifier mechanism and the gravity centre. The Takagi-Sugenofuzzy model for the non-linear system is expressed in Eq. (27).66 Distillation - Innovative Applications and Modeling

∑rj¼1 ωj zj ðtÞ ½Aj xðtÞ þ Bj uðtÞ _ ¼ xðtÞ (27) ∑rj¼1 ωj zj ðtÞ

where the weight ωj zj ðtÞ is 0 or a positive value, such that the sum of all the weights is positive; thus, the normalized weight, hi, is calculated in every rule from the zj membership functions in the Mjk set. It is well known by fuzzy logic that hj ¼ hj ½zðtÞ ≥ 0 and ∑rj¼1 hj ½zj ðtÞ ¼ 1, as expressed in Eq. (28).

ωj zj ðtÞ hj ½zj ðtÞ ¼ (28) ∑rj¼1 ωj zj ðtÞ

The system expressed in Eq. (27) is equivalent to the system in Eq. (29).

_ ¼ ∑rj¼1 hj ½Aj xðtÞ þ Bj uðtÞ

xðtÞ (29)

5.1. Application to a binary batch distillation column

In this chapter, the specific study case is a 12-tray distillation column, including a boiler and a condenser, using an ethanol-water mixture in a batch operation. In the Takagi-Sugeno fuzzy model the liquid (L) and vapour (V) molar flows are proposed as parameters; the nominal operating ranges in steady state are:

L ¼ ½0:418783, 2:97801 (30) V ¼ ½0:418783, 2:97801

According to these parameters, the Takagi-Sugeno fuzzy model that interpolates between four linear models based on the following rules is obtained:

6. Models experimental validation and comparison

The Takagi-Sugeno fuzzy model is validated in Matlab by using experimental data from a 12- tray batch distillation column with variable reflux, using an ethanol-water mixture and con- sidering the characteristics presented in Table 1.

Parameter Value Units

EtOH volume in boiler 2000 mL

H20 volume in boiler 2000 mL Process total pressure 637.42 mmHg

Table 1. Mixture initial parameters.

The initial molar composition of ethanol in the boiler is 0.2216, considering that the feed volume corresponds to 96%Vol ethanol. The characteristics of the process inputs for the study case, the heating power (QB) and the reflux valve opening (R) are shown in Table 2. Figure 3 presents the temperatures estimated by the Takagi-Sugeno model for the trays in the column body. The temperature increment and decrement due the reflux (R) action can be seen in all the trays. Figure 4 presents the temperature graphics corresponding to the condenser (a) and to the boiler (b) in the non-linear and Takagi-Sugeno model. Temperature variations existing during the heating power (QB) and reflux changes (R) are shown. It can be seen that there exist a difference between the results obtained by both models due the reflux action, this difference is provoked by the fixed operating points for liquid and vapour flows in the Takagi-Sugeno model; however, this difference is small (less than 1.5%). Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 69 http://dx.doi.org/10.5772/66760s

Table 2. Input parameters.

Figure 3. Plate temperatures in the distillation column.

In Figure 5, the composition graphics estimated for the distillation column trays by the Takagi-Sugeno fuzzy model are presented, these composition values vary according to the trayposition.In Figure 6, the simulation results obtained by the non-linear and Takagi-Sugeno models forthe light component composition in the condenser (a) and the boiler (b) are presented. It can beseen that the composition behaviour in both trays varies according the heating power (QB) andreflux (R) changes, as shown in Table 2.70 Distillation - Innovative Applications and Modeling

Figure 5. Plate temperatures in the distillation column.

Figure 7 shows the liquid and vapour molar flow behaviour during the distillation process. It can be seen the process dynamics when reflux or heating power changes exist. The error percentage in the Takagi-Sugeno model compared to the non-linear models, calcu- lated by the function shown in Eq. (45), is graphically represented in Figure 8. It can be seen that the error behaviour in the condenser (a) and the boiler (b) has a maximum value of 1.5% due to the reflux changes. Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 71 http://dx.doi.org/10.5772/66760s

Figure 7. Liquid and vapour molar flows.

72 Distillation - Innovative Applications and Modeling

Figure 8. a) Condenser and b) Boiler error percentages.

7. Conclusions

This chapter presents the analysis and design of a state-space non-linear model and the Takagi- Sugeno fuzzy model for a batch distillation column using a binary mixture. The state-space non-linear model is based on differential equations considering compositions, temperatures and molar flows in the column. The linear fuzzy model is based on four rules, considering as parameters the liquid and vapour molar flows.

Both, the state-space non-linear and the linear fuzzy models are simulated in Matlab consider- ing real input parameters (heating power and reflux) from a 12-tray batch distillation pilot plant using an ethanol-water mixture. The light component compositions and the tempera- tures in each tray of the column are calculated by both models. Besides, the obtained results are compared considering the same operating parameters, this comparison has the aim to verify the adequate functioning of the non-linear state-space and the Takagi-Sugeno models in order to analyse the existing differences. The Takagi-Sugeno fuzzy model presents small differences in the estimations of the composi- tion component and the tray temperatures when a reflux disturbance is presented due that the reflux affects directly the operating points established in this model; however, these differences are small enough to be neglected and both models converge under any operating condition. The Takagi-Sugeno fuzzy model for a distillation column represents an alternative tool that takes advantage of the fuzzy control theory, allowing to facilitate the design and implement nonconventional control strategies for non-linear systems, however, if a higher resolution response is required it could be convenient to consider the non-linear model. Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models 73 http://dx.doi.org/10.5772/66760s

Distillation: Basic Test in Quality Control of Automotive

Fuels

Ma Mercedes del Coro Fernández-Feal,

Luis R. Sánchez-Fernández andBlanca Sánchez-Fernández

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67140

Abstract

The petroleum-derived automotive fuels available on the market today have different characteristics from those that were available a decade ago, mainly due to the promotion of the use of biofuels. However, the study of their distillation curves remains a basic test for their quality control. The ISO 3405 Standard has been the basis of the test procedure for the determination of the distillation characteristics of petroleum-derived automotive fuels at atmospheric pressure. This test is essential for the quality control of this type of products because of the extensive information that can be extracted from the interpreta- tion of its results. The introduction of biofuels (bioethanol, biodiesel) in the new automo- tive fuel formulations, petrol and diesel fuels, made imperative to review ISO 3405:2000 in 2011. This paper studies the most significant changes between the two versions of the ISO 3405. The latest edition of the Standard is broader in scope; it has been modified in order to include the new fuel formulations which result from biofuel mixtures and the new criteria for repeatability and reproducibility calculation. This paper studies the most significant changes between the two versions of the ISO 3405 Standard together with a field study of commercial automotive fuel samples selection (with and without biofuel blend) and certified reference materials.

Keywords: distillation, volatility, quality control, fuel, biofuel

1. Introduction

‘Distillation is the most widely used separation technique in the petroleum industry’ [1].At present, petroleum remains the major source of energy resources, and for more than 100years, it has been the main source of fuels used in alternative internal combustion engines78 Distillation - Innovative Applications and Modeling

in auto-motion as well, both for spark ignition engines (SIE1), traditionally known as pet- rol engines, and for compression ignition engines (CIE2), or diesel engines. Nevertheless, we must bear in mind that differences in the operation of spark ignition and compression ignition engines require very different types of fuels. When we speak about petroleum-derived fossil fuels, used as automotive fuel, we must remember that in a given series of hydrocarbons the ignition temperature decreases as the molecular weight increases because the cracking of large molecules needs less activation energies [1], whereby: 1. The SIE require low boiling hydrocarbons, with a soft combustion temperature and a relatively high spontaneous ignition temperature. 2. In the CIE, hydrocarbons with low spontaneous ignition temperatures are preferable, whereby the compounds of low boiling points are unsuitable. From the chemical composition viewpoint, petrol is a blend of hydrocarbons between C4 and C11, with boiling points between 25 and 210°C and in which we can find all types of hydrocar- bons: paraffins, isoparaffins, olefins, aromatics, naphthenes, etc. They may also contain oxygen- ated compounds such as ethers (MTBE, ETBE, TAME3) and pure alcohols in variable proportions: minimum amounts of sulphur and nitrogen as well as additives (detergents, anti-knock, etc.).

From the chemical composition viewpoint, the diesel fuels are a blend of different compo- nents obtained from different refining processes, with a majority of hydrocarbons between C10 and C16, with boiling ranges between about 160 and 360°C, and low amounts of sulphur and nitrogen. Additives are also present in their formulations [2–4].

Petroleum is, even today, the source of energy most used worldwide, but it is not an inexhaustible source of energy; this fact, together with the need to protect the environment, has led to the search for new automotive fuels and for the modification of the characteristics of the existing ones. One of the paths chosen in recent years has been to include biofuels in the formulation of conventional automotive fuels given their great capacity for blend with petroleum-derived fuels [5]. Incorporating biofuels and/or bioethanol to petrol and biodiesel (FAME4) to diesel is a path to a more sustainable energy future and involves a great R&D effort since it is necessary to study how blending modifies fuel characteristics in the search for optimal behaviour in any automobile engine [6].

As a general rule, according to international specifications, petrol can be combined with bioeth- anol in a percentage not exceeding 10% by volume and diesel with biodiesel up to a maximum of 7% in volume without informing consumers about it. There are also specially designed vehi- cles that can support a mixture of petrol with 85% by volume of bioethanol (E85) and taxis or buses that use a mixture of diesel and biodiesel in a proportion of 70:30% by volume (B30) [7]. Now, any fuel which is in the market should guarantee that their use in an engine will pro- vide the projected energy performance that it will satisfy any other capacity inherent to their

use and it will perform to the environmental quality level required. In order to comply withthese conditions, those fuels must comply with certain specifications, i.e. a set of physical andchemical characteristics with maximum or minimum specified values, obtained through testprocedures or standards [8, 9], including their volatility.

With the aim of controlling engine performance and the formation of vapours which mayform explosive mixtures with air or escape to the atmosphere as emissions (VOCs—volatileorganic compounds), most of the specifications for petroleum distillate products, specially themain automotive engine fuels, limit the values of certain distillation characteristics (volatility).A fuel distillation range provides decisive information about its composition, its use and itsbehaviour during storage.

2. State of the art

2.1. Volatility versus fuel type

Among the wide variety of features to consider when establishing the quality of a fuel usedin auto-motion, volatility stands out as one of the most critical ones since it is a characteristicdirectly related to engine performance and pollutant emissions [2–4].

2.1.1. Petrol

Petrol is a fuel which is a liquid state in the fuel tank and in the fuel injectors (or carburettor onolder engines) and which is nebulized with air before being injected into the combustion chamber:• If the volatility of fuel is low, the petrol does not exist in the gas phase, and there will be dif- ficulties with the starting up of the engine and the behaviour of the engines in cold regimes.• If the volatility is high, the petrol can be vaporized in the tank itself or in the pipelines (‘vapour lock’). As a consequence the injection rate is inadequate, and the engine drowns.

2.1.2. Diesel

The volatility characteristics of a diesel have a great influence on the performance of diesel engines:

• If the volatility is low, then high distillation end points are obtained, which are indicative of high combustion times and poor combustion of heavy hydrocarbons. This will lead to the formation of smoke, loss of power and increased fuel consumption.• If the volatility is high, then the fuel can cause incidents of ‘vapour lock’ in the lines.

2.2. Measure of volatility: distillation curve

Volatility is not a physical magnitude that can be measured directly; it is necessary to definemethods of evaluating it. One universally used method to determine the volatility of a fuel isthe distillation test [10, 11] that offers different information according to the type of fuel tested.80 Distillation - Innovative Applications and Modeling

2.2.1. Petrol

The distillation test measures the percentage of vaporized fuel as the temperature increases. The test result is a curve obtained under standardized conditions of temperature versus per- centage of evaporated fuel (Figure 1) wherein the different sections of the curve allow us to interpret the different behaviours of the product:

• At least 20% V/V fuel must be vaporized below 70°C to ensure good cold start capability. If this percentage is lower, then difficulties may occur at start-up; if it is too high, evaporation losses will occur in the fuel tank, and vapour bubbles may form in the intake manifold of the vehicle. • The temperature at which 50% V/V of fuel is vaporized is a critical parameter, since if it is too low it can cause the solidification of water vapour contained in the intake air resulting in formation of ice on elements forming the blend. • If the temperature at which 90% V/V of the fuel is vaporized is too high, then the fuel can remain in liquid form within the cylinder, displacing the lubricant and coming to cause oil dilution. Additionally, combustion may be hampered, causing irregular operation of the engine. Also, the presence of hydrocarbons of high boiling point in the petrol is decisive for the generation of polluting emissions.

Figure 1. Distillation curve of petrol.

The percentages of fuel evaporated at 70, 100 and 150°C are limited. Additionally, a limita- tion in the final boiling point of to 210°C is also implemented in the regulations, ensuring the complete combustion of hydrocarbons and the non-formation of deposits in the combustion chamber and spark plugs.

2.2.2. Diesel

In a CIE, the volatility problems that may be present are notably different from those in SIE. In the regulations, there are no limitations in the light section of the curve but only for the end zone, where the fractionation of the components occurs. Distillation: Basic Test in Quality Control of Automotive Fuels 81 http://dx.doi.org/10.5772/67140

The distillation test, in this case, measures the percentage of fuel which is recovered as thetemperature increases. The test result is a curve obtained under standardized conditions oftemperature versus percentage recovered (Figure 2). In these, fuel is important to note:• The temperature at which vaporization ends, since if this is very high, combustion of the less volatile components will be incomplete, fuel droplets may reach the cylinder walls and dilution of the lubricating oil may take place, thereby increasing wear and producing coke deposits in the combustion chamber and waste segments [3].• The end point of the fractionation of the components. This parameter is established so as 65% V/V must not have distilled before 250°C; 85% V/V should be distilled before 350°C,and 95% V/V before 360°C.

Figure 3. Comparison between distillation curves of petrol and diesel.

ISO 3405 International Standard has been adopted by the European Standard EN ISO 3405, and it received the rank of the National Standard, by publication in the national language of an identical text under the responsibility of a member of CEN (European Committee for Standardization): UNE-EN ISO 3405 (Spain), DIN-EN ISO 3405 (Germany), etc. This procedure aims to establish the steps ‘for determining the distillation characteristics of light and middle distillates derived from petroleum having initial boiling points above 0°C and end points below approximately 400°C’. There are standards similar to ISO 3405 developed by other agencies with the same objective, such as ASTM D86: Standard Test Method for Distillation of Petroleum Products and Liquid Fuels at Atmospheric Pressure, whose first version dates from 1978, or IP 123: Petroleum Products—Determination of Distillation Characteristics at Atmospheric Pressure. The test samples are classified into ‘groups’ based on their composition and the characteristics of expected volatility. In the case of fuels for automotive engines, petrol with up to 10% V/V ethanol is included in Group 1 and diesels with up to 20% V/V biodiesel in Group 4 (Table 1). Belonging to a particular group defines the setup of the equipment to be used and the con- denser temperature. Finally, it determines the operation conditions to be used in the process of distillation by ISO 3405 (Table 2).

Group 1 Group 4 Type of sample Petrol Diesel

Reid vapour pressure (kPa) ≥65.5 <65.5

Characteristics of expected volatility

Initial distillation point, IDP (°C) – >100

Final boiling point, FBP (°C) ≤250 >250

Table 1. Sample type by group and expected volatility characteristics.

Group 1 Group 4 Temperature of condensador bath (°C) 0–1 0–60

Temperature of medium around recovered receiving 13–18 ±3 of charge

cylinder (°C)

Time from the first heat to IBP (min) 5–10 5–15

Time from IBP to 5% (V/V) recovered (s) 60–100 –

Uniform average rate from 5% (V V) of recovered to 5 mL 4–5 4–5

in the flask (mL/min)

Time from 5 mL residue in the flask to FBP (min) ≤5 ≤5

During the testing process, a 100 mL test portion is distilled under the specified conditionsappropriate to the fuel group, and systematic observations of thermometer readings and vol-umes of condensate recovered are made.

2.4. Precision ISO 3405: automated apparatus

The introduction of new formulations in automotive fuels made necessary the adaptation ofthe standard in effect at the time of their appearance (ISO 3405:2000), and, given the volatilitycharacteristics of the new formulations, it was also necessary to validate the test method againbased on new precision criteria.The new version of the ISO 3405 standard (2011) establishes new criteria, based on the group towhich it belongs the sample tested, to determine the validity of two results obtained under thesame conditions by one operator using the same apparatus, in the same operating conditions, onthe same day, on identical samples (repeatability, r) or obtained by different operators workingin different laboratories on identical material test (reproducibility, R).In the case of petrol and bioethanol blends (Group 1), these criteria are listed in Tables 3 and 4and in the case of diesel and biodiesel blends (Group 4) in Tables 5 and 6.

2000 Evaporated % (V/V) 2011

Repeatability Group 1 Repeatability Group 1 Valid range (°C)

3.9 IBP 0.0295 (E + 51.19) 20–70

r2 + 0.56 10 1.33 35–95

r2 50 0.74 65–220

r2 90 0.00755 (E + 59.77) 110–245

4.4 FBP 3.33 135–260

r2 is a constant function of the slope, ∆C/∆V, at each distillation point, with values calculated from r2 = 0.673 (∆C/∆V) + 1.131.E is the temperature at the percentage evaporated within the prescribed valid range.

Table 3. Repeatability (Group 1).

2000 Evaporated % (V/V) 2011

Repeatability Group 4 Repeatability Group 4 Valid range (°C)

3.5 IBP 0.018 T 145–220

1.42 (∆C/∆V) + 1.2 10 0.0094 T 160–265

1.42 (∆C/∆V) + 1.2 50 0.94 170–295

1.08 (∆C/∆V) + 1.1 90 0.0041 T 180–340

1.08 (∆C/∆V) + 1.1 95 0.01515 (T–140) 260–340

3.5 FBP 2.2 195–365

Slope: ∆C/∆VT is the temperature at the percentage recovered within the prescribed valid range.

Table 4. Repeatability (Group 4).

84 Distillation - Innovative Applications and Modeling

2000 Evaporated % (V/V) 2011

Reproducibility Group 1 Reproducibility Group 1 Valid range (°C)

7.2 IBP 0.0595 (E + 51.19) 20–70

R2 + 0.72 10 3.20 35–95

R2 50 1.88 65–220

R2 – 1.90 90 0.019 (E + 59.77) 110–245

8.9 FBP 6.78 135–260

R2 is a constant function of the slope, ∆C/∆V, at each distillation point, with values calculated from R2 = 1.998 (∆C/∆V) + 2.617. E is the temperature at the percentage evaporated within the prescribed valid range.

Table 5. Reproducibility (Group 1).

2000 Evaporated % (V/V) 2011

Reproducibility Group 4 Reproducibility Group 4 Valid range (°C)

8.5 IBP 0.055 T 145–220

2.64 (∆C/∆V) + 3.0 10 0.022 T 160–265

3.97 (∆C/∆V) + 2.9 50 2.97 170–295

2.53 (∆C/∆V) + 2.0 90 0.015 T 180–340

2.53 (∆C/∆V) + 2.0 95 0.04227 (T–140) 260–340

10.5 FBP 7.1 195–365

Slope: ∆C/∆V T is the temperature at the percentage recovered within the prescribed valid range.

Table 6. Reproducibility (Group 4).

3. Materials and methods

Step 1. A sample selection of automotive fuel (petrol, diesel) with and without blend of biofuel (bioethanol, biodiesel) for a field study is used. The variations in product volatility as a result of the presence of biofuel in its composition are checked.

Each sample is tested in duplicate by two operators.

Step 2. The changes in criteria established for repeatability and reproducibility in Standard ISO 3405 are studied; certified reference materials are used. Distillation: Basic Test in Quality Control of Automotive Fuels 85 http://dx.doi.org/10.5772/67140

3.1. Test description

3.1.1. Reagents and materials

• Acetone: cleaning solvent.

• Certified reference material (CRM).• Distillation flasks: flasks should have a capacity of 125 mL and be constructed of heat-re- sistant glass, according to the dimensions and tolerances given in Standard ISO 3405:2011.• Receiving cylinder: graduate cylinder of 100 mL capacity, with a mark at 100 mL and metal base.• Residue cylinder of 5 mL capacity.• Certified temperature-sensor pt100 to an accuracy of 0.01C.• Centring device, for centring the temperature sensor, adjusts the neck distillation flask, al- lows to centre the temperature sensor and prevents steam leaks.

3.1.3. Preparation of apparatus

• Clean the condenser tube, employing acetone. Dry thoroughly to remove any portion of acetone used for cleaning the device.• Check that the temperature probe is properly seated in the centring device. Check your state and proper cleaning.• Choose the support plate of the flask as the orifice diameter thereof according to the type of sample to be tested (Table 7).• Check that the value of atmospheric pressure recorded by the apparatus is coincident with that indicated by the recording barometer atmospheric pressure in the laboratory. Group 1 Group 4Diameter of hole in flask-support board (mm) 38 50

Temperature at start of test (°C)

Flask and thermometer 13–18 ≤ambient

Flask-support board and shield ≤ambient –

Receiving cylinder and sample 13–18 13 at ambient

• Measure the test portion precisely to the 100 mL mark of the receiving cylinder, and then transfer it as completely as practical to the distillation flask, taking care that none of the liquid flows into the vapour tube. If irregular boiling (bumping) is expected, add a small volume of clean and dry boiling chips to the test portion. • Fit the flask vapour tube, provided with a silicone rubber stopper, tightly into the condens- er tube. Adjust the distillation flask in a vertical position so that the vapour tube extends into the condenser tube for a distance of 25–50 mm. Raise and adjust the flask-support board to fit snugly against the bottom of the flask. • Fit the receiving cylinder with a drip deflector, through which the distillate is going to drip.

• Place the receiving cylinder that was used to measure the test portion, without drying, into the bad under the lower end of the condenser tube so that the end of the condenser tube is centred in the receiving cylinder and extends therein for a distance of at least 25 mm.

After the choice of the method, which has been specifically developed to the distillation test according to Table 2 and the corresponding group, follow the steps indicated by the system software. Any distillation that does not meet above conditions must be repeated, as well as those in which the actual loss differs by more than 2 mL from the estimated value.

3.1.5. Calculations

The data required for calculations is recorded in the range between the initial and the final boiling point, with an accuracy of 0.1 mL for all the readings on the receiving cylinder and with an accuracy of 0.1°C for all the readings on the temperature sensor.

Distillations carried out with automated instrument do not require manual calculation; the system software makes the appropriate calculations according to the corrective measures established by the Standard. However, it is certainly right to check the atmospheric pressure value does not differ by more than ±10 hPa from the value provided by the barometer in the laboratory.

3.2. Results obtained

3.2.1. Step 1: Samples of petrol—distillation curves obtained

Distillation test is carried out on 24 petrol samples with a bioethanol percentage that var- ies between 0.0 and 4.0% V/V, obtaining their corresponding distillation curves. Among these curves, we have selected seven for being analyzed and included in the present paper. Obtained results are shown in Figure 4.

After studying the trend and as the different sections of the curve give the opportunity to interpret the different product performances, a particular observation of each section is devel- oped, making a graphic comparison on the basis of an average value (Figures 5–7). Distillation: Basic Test in Quality Control of Automotive Fuels 87 http://dx.doi.org/10.5772/67140

3.2.2. Step 1: Diesel samples—distillation curves obtained

Distillation test is carried out on 24 diesel samples which contain a different biodiesel percent-age (FAME), obtaining their corresponding distillation curves. Among these curves, we have88 Distillation - Innovative Applications and Modeling

selected seven for being analyzed and included in the present paper; six of them correspond to diesel samples with a usual biodiesel percentage, between 0.0 and 7.0% V/V. However, the other one corresponds to a diesel sample with a 30% V/V biodiesel percentage; this is outside the Standard scope. Obtained results are shown in Figure 8.

As in the case of petrol samples, here we study the trend and the different sections of the distil- lation curve. However, in this case, the distillation curve will be divided for its study in two different sections: the first one comprises from the initial distillation point until 60% of the total volume is collected, whereas the second one comprises from this point to the final distillation point. A graphic comparison on the basis of an average value is also used here to illustrate the results, making a graphic comparison on the basis of an average value (Figures 9 and 10). Distillation: Basic Test in Quality Control of Automotive Fuels 89 http://dx.doi.org/10.5772/67140

3.2.3. Step 2: Repeatability and reproducibility

In order to know and be able to check the quantitative change derived from the precision require-ment set in the new edition of the Standard, which involves repeatability and reproducibility,90 Distillation - Innovative Applications and Modeling

two different certified reference materials are used; one of them matches with the petrol boiling range, whereas the other one matches with the diesel boiling range.

Two analysts are involved in the test process; each using a different distillation automated equipment, in the same laboratory, and maintaining the required operation conditions for the standardized calculation. Distillation test is carried out in duplicate, and their results are shown in Figures 11–14.

Figure 11. Quality control according to ISO 3405:2000; petrol-CRM.

Figure 12. Quality control ISO 3405:2011; petrol-CRM.

Figure 13. Quality control according to ISO 3405:2000; diesel-CRM.

92 Distillation - Innovative Applications and Modeling

Figure 14. Quality control according to ISO 3405:2011; diesel-CRM.

4. Discussion

4.1. ISO 3405:2011 versus ISO 3405:2000

The fourth edition of ISO 3405 Standard came into force on 15 January 2011. This fourth edi- tion cancelled and replaced the third edition, which had come into force on 1 March 2000. It is noteworthy that the text of this new edition is in line with the American Standard ASTM D86, widely used throughout the petroleum industry. The fourth edition of ISO 3405 Standard introduces significant changes which are the result of the new formulations of automotive fuels and which are listed below:

The latest edition of the Standard is wider in scope. It has been modified in order to include the new fuel formulations, obtained from mixtures of biofuels and petrol (containing up to 10% V/V of ethanol) and diesel (containing up to 20% V/V of biodiesel). Additionally, it estab- lishes a clear definition of ‘light distillates’ and ‘middle distillates’. Petrol from direct distillation (the petroleum fraction obtained by distillation at atmospheric pressure) no longer has their own group (the former Group 0, since the latest edition of the Distillation: Basic Test in Quality Control of Automotive Fuels 93 http://dx.doi.org/10.5772/67140

Standard refers only to four distillation Groups 1, 2, 3 and 4), instead of the former five Groups0, 1, 2, 3 and 4. Petrol and their mixtures with bioethanol belong to Group 1, while diesel andtheir mixtures with biodiesel belong to Group 4.

This Standard specifies an assay method, utilizing either manual or automated equipment.However, its latest edition sets the automated alternative as the reference method in the eventof a dispute, unless otherwise agreed.

The latest edition of the Standard includes a specific point related to the test procedure utiliz-ing automated equipment. Although the former edition allowed the use of this type of equip-ment, the procedure had not been defined so far. Nowadays, most distillation tests are carriedout utilizing automated equipment. Once programmed, the procedure is performed in anautonomous way by the instrument, but programming them is not easy. It requires an abso-lute control and knowledge of the process as well as of the conditions required for each specificsample. The validity on the findings remains dependant on performing a validation study.The latest edition of the Standard requires the establishment of new criteria for calculatingrepeatability and reproducibility.

The latest Standard specifies the percentages of distillate required at specific temperaturesfor petrol. Accordingly, the Standard includes a normative annex (Annex C) which providesvalues of reproducibility of petrol percent volume evaporated at 70, 100, 150 and 180°C. Thesereproducibility statements were estimated for the specification temperatures and percentagesfrom the data collected in an inter-laboratory study:• E70 → R = 2.7% V/V.

• E100 → R = 2.2% V/V.

• E150 → R = 1.3% V/V.

• E180 → R = 1.1% V/V.

4.2. Biofuel impact on fuel volatility

4.2.1. Petrol

As we set before, the petrol distillation curve study was developed through its analysis in threedifferent sections. From the study of the two first sections (IBP-E20; E20-E70), we conclude thatthe evaporated percentage is higher in blends. So, in the range between 30 and 90°C, whichcomprises from IBP to the middle boiling point, the petrol volatility increases from bioethanoladdition. In the final section, the sample distillation curves coincide to a great extent, and thereare no any significant changes, as might be expected from the bioethanol boiling point.

4.2.2. Diesel

For diesel blends, containing up to 7% V/V biodiesel, the study of the distillation curve indi-cates the recovered percentage has risen slightly in the first section, while we can observe abigger variation in the last one, where the fractioning of the heavy components of the samplestakes place; this is between R90 and R95.94 Distillation - Innovative Applications and Modeling

Diesel blends, containing 30% V/V biodiesel, are outside the ISO 3405:2011 Standard scope. Distillation test has been carried out, considering them as part of Group 4 and, then, accord- ingly to the conditions established for that group.

Distillation curve for diesel blends, containing 30% V/V biodiesel, indicates clearly the volatil- ity diminution from the own characteristics of the biodiesel: high boiling point and low vola- tility (Figure 15). As in this type of products, the volatility diminution is directly related to the viscosity; the use of this type of blends in the engines is intimately related to their operation and performance.

Figure 15. Diesel distillation curves, 0.0% V/V and 30.0% V/V FAME.

4.3. Estimation of variation suffered by the accuracy of the automated method based on criteria of repeatability and reproducibility.

The latest edition of the Standard, ISO 3405:2011, establishes new repeatability and reproduc- ibility criteria. This new criteria has reduced measure variations allowed in the whole range, affecting petrol (Group 1) and diesel (Group 4). Relatively small variations are allowed in the middle section of the distillation curve, whereas a more significant variation is allowed in the IBP and FBP determination, as shown in Figures 16 and 17.

4.4. Future prospects

The EU has promoted turning plants into fuel as a way to reduce carbon emissions from transport for the last 10 years. Today however, some say that biofuels have become part of the problem and actually have generated more CO2 than they saved, as the demand for crops needed to produce them has led to the destruction of forests. The EU now wants to limit the amount of fuel produced from food crops and shift to biofuels that are produced from non- food sources, such as waste. Distillation: Basic Test in Quality Control of Automotive Fuels 95 http://dx.doi.org/10.5772/67140

Figure 16. The values of repeatability and reproducibility for the same petrol-CRM, according to ISO 3405:2011 and ISO3405:2000.

Figure 17. The values of repeatability and reproducibility for the same diesel-CRM, according to ISO 3405:2011 and ISO3405:2000.

The EU is committed to meeting 10% of its transport fuel needs from renewable sources,mostly biofuels, by 2020. But pressure is growing to change this policy by limiting the amountof food-based biofuels.

In response to these concerns, the European Parliament voted in favour of a compromise dealwith the Council to limit the amount of fuel produced from food crops such as rapeseed andpalm oil. The new legislation will enter into force in 2017 [12].

The future liquid automotive fuel formulations will remain dependant on distillation testas a powerful quality control tool. It provides useful information, which can be employedto establish optimal conditions of use in the appropriate engines, as well as to establish safeconditions for storage, transportation and delivery.

5. Conclusion

In 2011, the addition of up to 10% V/V bioethanol in petrol and up to 20% V/V of bio-diesel in diesel, as a result of biofuel promotion, has prompted a careful review of the96 Distillation - Innovative Applications and Modeling

1. The broadening of the scope to cover these new products

2. The adjustment of the calculations related to the method accuracy

Standard relating to test standardization, which establishes the procedure to determine the distillation characteristics of petroleum products at atmospheric pressure, remains open to future review and updating.

Enhanced Distillation Under Infrared Characteristic

Radiation

Kuo-Ting Wang, M. Quinn Brewster and

Wei-Hsiang Lai

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67401

Abstract This chapter introduces quasi-steady water vaporization under mid-infrared (IR) radia- tion and the IR absorption of characteristic radiation associated with the first-kind liquid-gaseous phase transition of water. When characteristic radiation in the mid-IR spectral range is applied to water surface, the strong volumetric absorption of radiation energy in the liquid-phase causes water to be nearly isothermal. In addition to volumet- ric absorption, surface absorption of characteristic radiation induces vaporization of water. The complete mechanism of liquid-gaseous phase-transition radiation involves the direct surface absorption/emission of infrared energy accompanied by evaporation/ condensation of water. A direct consequence of excess characteristic radiation upon water surface is the induced supersaturation. This mechanism opens up a door for enhanced distillation under characteristic radiation. Blackbody-like materials such as black anodized aluminum surfaces and metal surfaces painted in black are recommended to be heated to ~250 C to serve as economical radiation sources. For isothermal water at room temperatures, ~20% supersaturation can be induced by hemispherical Blackbody radiation with temperature ~11 C higher than the water temperature. In this situation, energy extracted from the ambient for water vaporization can be as much as 80% of latent heat. With radiation-enhanced evaporation, the production cost for distilled water is signifi- cantly reduced as compared to distillation at the boiling point.

While latent heat of evaporation is a fixed amount of energy needed to vaporize liquid-water, how energy is supplied to cause evaporation is an open area for engineers to explore to achieve their design goals. Evaporation is a process that water molecules go through the phase transi- tion of the first kind from the liquid phase to the gaseous phase. This process is driven by the concentration gradient of water molecules on the vapor side of the water surface. When water is heated up to the boiling point, the saturation pressure of water is increased to exceed the ambient water-vapor pressure not only on the water surface but also in the bulk so that “evaporation” (boiling) takes place everywhere in the water. For water purification purposes, water can be distilled in this way. One advantage of this type of water purification is that distillation can be quickly carried out by supplying sufficient heat. However, one obvious disadvantage at the same time is that a significant amount of energy is lost to the ambient in order to maintain water temperature at the boiling point. This chapter suggests another way of distillation that enables water to be supersaturated on the surface so as to enhance evaporation. This method utilizes the mechanism of so-called phase-transition radiation to enhance evaporation without requiring water to reach the boiling point. Since liquid-water molecules are constantly experiencing breaking and formation of hydrogen bonds due to intermolecular vibrations, there are moments when some water mole- cules are weakly bonded. When photons hit such molecules on the surface, the photons that carry enough energy to break the hydrogen bond will be absorbed to cause transitions of energy states, namely evaporation. The spectral range of the evaporative absorption defines the spectrum of characteristic radiation, which is in the mid-IR range. A good amount of effort [1] has been spent on the characteristic wavelength of phase-transition radiation in vapor condensation process. Quasi-steady equations for radiation absorption in semi-infinite liquid-water as well as their dilute approximations are presented in this chapter. Semi-infinite liquid-water is selected to represent a common scenario for engineering distillation applications. These equations deal with liquid phase, vapor phase, and the vapor liquid interface in the presence of IR character- istic radiation. In addition to volumetric absorption of radiation, which is commonly recog- nized as far as radiative heat transfer is concerned, surface absorption of radiation is taken into account in the liquid-phase equations. Based on the IR absorption characteristics in the liquid- water, the liquid phase is essentially isothermal under moderate radiation strength in the mid- IR range. In the equations for vapor phase and interface, the situation of supersaturation triggered by an excess amount of IR characteristic radiation is presented for the first time. Enhanced evaporation as a result of supersaturation is exemplified in dilute systems. Although the enhanced evaporation rate by IR radiation may not be as fast as that of the traditional way of boiling water, this method is more energy efficient and economical when continual distilla- tion is needed for a larger amount of water.

In the last section of this chapter, the theory of phase-transition radiation is extended to the situation of supersaturation for semi-infinite water. The evaporation flux due to phase- transition radiation is linked to characteristic radiation and supersaturation. The equation for Enhanced Distillation Under Infrared Characteristic Radiation 101 http://dx.doi.org/10.5772/67401

quasi-steady supersaturation is obtained and used to close the mathematic problem whenvapor pressure at water surface is no longer subject to saturation conditions.

2. Quasi-steady semi-infinite water

2.1. Liquid phase

A sketch for the thermodynamic system of semi-infinite water is shown in Figure 1. In theliquid phase, the temperature distribution is subject to three heat transfer modes: conduction,convection, and radiation,

2.1.1. Nondimensionalization For small temperature changes (i.e., a few degrees C), physical properties (Ka, kl, C, fs) can be assumed to be constant and a general form for the liquid-phase equation is obtained following a nondimensionalization analysis with,

δr ¼ 1=Ka , δt ¼ kl = m_ ″ C , x ¼ x=δr ,

ΔT max ¼ 1 f s qr, s = kl δr 1 δt 1 , T ¼ ðT T s Þ=ΔT max , ð5Þ

d T δr dT 2 δr x þ þ 1 e ¼ 0: dx2 δt dx δt

In Eq. (5) different scales for length (characteristic length for IR absorption δr and convective length scale δt) as well as temperature (ΔTmax) [2] are used to formulate the nondimensional form. Based on two different kinds of BCs, two different forms of solutions are obtained,

General solution: T ¼ A þ Bexðδr =δt Þ ex (A, B: constants);

2.1.2. Isothermal water under mid-IR

Based on the mid-IR absorption spectrum of liquid-water, water is fairly opaque under mid-IR radiation and the attenuation of mid-IR radiation occurs within only several microns [2]. The characteristic length for IR absorption δr (which is inversely proportional to the absorption coefficient) is much smaller than the convective length scale of water δt in typical conditions. As a result, the convection term in the liquid-phase temperature equation can be ignored. The simplified equation has the following form,

δr d2 T ≈ 0 ) 2 þ ex ≈ 0, ΔT max ≈ 1 f s qr, s δr =kl ; ð6Þ δt dx

and the same simplified solution for both Cases 1 and 2,

Eq. (7) leads to an important feature for liquid-phase quasi-steady temperature distribution:water is essentially isothermal under mid-IR radiation with moderate strength [2], as illus-trated in Example 1.

The liquid-phase enthalpy changes from the top (x = 0) to the bottom (x ! ∞) can be describedin terms of conductive and radiative heat transfer by applying integration to Eq. (4) from x = 0 tox ! ∞:

where the ratio of air molecular weight to vapor, M2/M1 = 28.97/18 = 1.61, and the partial pressureof vapor P1 = (RH) (Psat). This form of m1 and its dilute approximation are listed in Table 3.Reference values for air molecular weight and other properties are available at [3].104 Distillation - Innovative Applications and Modeling

2.2.2. Mass transfer of water vapor

The transport of water vapor can be divided into two parts: the microscopic molecular diffu- sion and the macroscopic convection. When vapor mass fraction is much less than unity, i.e., m1 << 1, the macroscopic convection term is often negligible, leaving the diffusion term described by Fick’s law in the dilute system. Mass flux of water vapor is described by, dm1 m_ ″1 ¼ m1 ρv ρD : ð10Þ |ﬄﬄ{zﬄﬄ} dy convection |ﬄﬄﬄﬄﬄ ﬄ {zﬄﬄﬄﬄﬄ ﬄ } diffusion

where Lewis number Le = D/α and thermal diffusivity α = k/ρCp. Numerical values of Le for dryair and saturated air at different temperatures are tabulated in Table 4 and plotted in Figure 2.The algebraic formula for α can be found in Table 1 with the corresponding curve-fit coeffi-cients available in Table 2 [5].The heat flux equation can be simplified if any of the following conditions are valid: (1) dilute; (2)nearly equal enthalpy for two species; (3) Le ≈ 1, which is generally true for air-vapor mixturesunder atmospheric conditions. The condition of nearly equal enthalpy is achievable with prop-erly chosen reference enthalpies for air and vapor. To achieve this condition, enthalpies of liquid-water and vapor are taken from steam tables and the reference enthalpy of air is set to h2,ref = 2501kJ/kg at Tref = 0 C to give,

Figure 2. Lewis number, Le, for saturated air and dry air at one atmosphere. Numerical values are shown in Table 4.

h1, u ½kJ=kg ≈ 4:2T ½ C: ð15Þ

This leads to a simplified heat flux equation,

and its quasi-steady equation,

Dilute approximations for mixture enthalpy h and specific heat Cp are listed in Table 3. Algebraic forms for air enthalpy h2 and specific heat Cp,2 are tabulated in Table 1. Curve-fit coefficients for Cp,2 are placed in Table 2 [5].

2.3. Vapor-liquid interface

Vapor-liquid interface equations are obtained by matching the mass flux of species 1 (vapor or liquid-water) and energy flux at the interface. Mass flux of species 1: Enhanced Distillation Under Infrared Characteristic Radiation 107 http://dx.doi.org/10.5772/67401

Together with the mass diffusion equation (11), mass flux can be solved for,

00 ρD m1, s m1, e m_ ¼ lnð1 þ Bm Þ, Bm ¼ : ð19Þ L 1 m1, s

Its dilute approximation is listed in Table 3.

Heat flux:

Eq. (20) is based on enthalpy formulation. Alternatively, the heat flux equation can be obtainedbased on temperature formulation without approximations,

Based on Eq. (20) and the heat diffusion equation (17), an alternative form for mass flux can beobtained to relate it to heat transfer variables,

At the first glance evaporation flux in Eq. (22) seems to be influenced by fs. However, itsdependency on fs is eliminated [2] when the energy balance for the entire liquid is taken intoaccount as done in Example 2, giving,

he hs Bh ¼ : ð23Þ hs h1, o þ qr, s =m_ ″

The corresponding dilute approximation for mass flux is shown in Table 3.

Given (RH)e, these two forms of mass flux are instrumental in evaluating surface temperatureTs—even without the knowledge of the vapor layer thickness L. For an isothermal dilutesystem (see approximated forms in Table 3), an implicit form for Ts is obtained by equatingthe two mass-flux forms, giving,108 Distillation - Innovative Applications and Modeling

ðRH Þs Psat, s ðRH Þe Psat, e Cp 1

Psat, s Psat, e ðRH Þe 1:61Cp ðT e T s þ T r, s Þ

≈ þ ; ð25Þ P P ðRH Þs ðRH Þs Le 2501 3:2T s

in which the unit for temperature (i.e., for Te, Ts, and Tr,s) is [ C]. Figure 2 shows the relation- ship of Lewis number Le with T and RH at one atmosphere. For evaporation taking place at a moderate-temperature (0–40 C) under atmospheric conditions, Le ≈ 1.18 appears to be a good approximation for water vapor-air mixtures.

2.4. Supersaturation by characteristic radiation

transition radiation is accompanied by a continuous absorption band. The “band” feature of the characteristic radiation is primarily a result of the convolution of population distributions for translational energy and rotational energy of vapor molecules. Since vapor molecules can be treated as a continuum in atmospheric conditions, the population distribution of translational energy at thermodynamic equilibrium is described by the Maxwell-Boltzmann distribution. Consequently vapor molecules are continuously populated as demonstrated in Figure 3. Descriptions for this model can be found in [1]. Intermolecular vibrations of water molecules in the liquid phase broaden the characteristic radiation band and smooth out its far wings.

Although the peak value of the population distribution function is slightly brought down as aresult of the broadening at the lower energy state, a previous work [6] has shown that the shapesof population distributions with and without invoking broadening effects of intermolecularvibrations in liquid-water are similar to each other.For modeling purposes, vapor molecules are distributed over a continuous band by energyconvolution and liquid-water molecules are treated as at the same energy level to simplifymathematical formulations. In other words, the broadening of the lower energy state isignored. Modeling intermolecular vibrations of water molecules is in fact a very challengingtask because the hydrogen bonds, which directly affect intermolecular vibrations, are con-stantly breaking and forming and are highly dependent on temperature.Since mathematical forms for population distribution functions for vapor molecules have beenestablished in the previous work [6], their derivations are skipped in this chapter. Togetherwith population distribution functions and related parameters, equations for evaporationfluxes related to absorption, spontaneous emission, and induced emission are outlined inTable 5.

2.4.2. Characteristic wavelength

Population distributions in Figure 4 suggest the active spectral range for characteristic radia-tion. For T = 0–100 C characteristic wavelength peaks at 5–6 μm in the mid-IR range, which isoutside the visible spectrum. Figure 4 is a duplicate of wavelength-based population distribu-tions H(λ, T) in [1] for vapor molecules with respect to the transition with one hydrogen bond(HB) breaking/formation. The integration of the population distribution function over theentire wavelength range is unity by definition and is confirmed through numerical tests.

2.4.3. Evaporation flux equations

Phase-transition radiation involves three energy transition modes when photons interact withwater molecules on the vapor-liquid interface: absorption, spontaneous emission, and inducedemission. Evaporation fluxes related to these three modes for vapor molecules, Ng″ [#/m2-s],can be associated with phase-transition radiation through (1) collision rates of water moleculesand photons at the interface and (2) Einstein’s coefficients. To avoid lengthy descriptions,evaporation flux equations are tabulated in Table 5. The spirit of these equations is that whenphotons interact with water molecules at the interface, there are chances for phase transitions

Figure 4. Population distribution functions of vapor molecules at different temperatures (duplicated from [1]).114 Distillation - Innovative Applications and Modeling

2.4.4. Supersaturation by characteristic radiation

Assuming ideal gas for water vapor and using overbar to indicate saturation conditions, vapor number density ng is related to supersaturation s via, ng ¼ng ð1þsÞ. Saturated air with 100% relative humidity is equivalent to “zero” supersaturation.

The collimated radiation Iλ can be regarded as an excess radiation in addition to the back- ground Blackbody radiation at thermodynamic equilibrium. If Iλ is taken away from Eq. (26), the net evaporation flux will automatically vanish to satisfy thermodynamic equilibrium conditions. Since s is a finite number, a simple form for evaporation flux is obtained assuming that spontaneous emission dominates the emission contribution in Einstein’s relation (which is based on thermodynamic equilibrium conditions), giving, Enhanced Distillation Under Infrared Characteristic Radiation 115 http://dx.doi.org/10.5772/67401

2.4.6. Supersaturation = 0Local thermodynamic equilibrium (LTE) with s = 0 can be assumed when the collimatedincident radiation Iλ is much weaker than Blackbody radiation Ib,λ. This leads to a muchsimpler form for the net evaporation flux in λ ! λ + dλ, !

Eq. (29) can also be interpreted as the fraction of radiation absorbed at interface [2].Einstein’s coefficient of spontaneous emission a21 is a small number on the order of 107 to 108[10, 11]. With a21 = 3 108 [10] Eq. (29) is plotted in Figure 6. Readers shall not be bothered bythe peaks of fs between 2.5 and 3 μm because the evaporative flux in Eq. (28) is predominantlysubject to the population distribution function Hλ.

2.4.7. Supersaturation 6¼ 0If the collimated radiation is of moderate strength (i.e., not large enough to break LTE),absorption of excess radiation may result in elevated evaporation flux and thus supersatura-tion. Eq. (27) in λ ! λ + dλ can be written in terms of fs,

2.4.8. Quasi-steady supersaturation

Relation between supersaturation and incident radiation can be established for a thermody-namic system at quasi-steady state. Consider such a system originally at quasi-steady statewithout excess IR radiation to drive out water molecules from the surface and that there isneither curvature effects nor salutes to exert additional influences on equilibrium pressure.Vapor pressure at interface is just the saturation pressure at the surface temperature. As soonas an additional mid-IR radiation field is applied to the system, the evaporation rate begins to116 Distillation - Innovative Applications and Modeling

Figure 6. Surface absorption efficiency fs.

exceed the condensation rate, and more vapor pressure starts to build up on water surface before vapor diffuses away. This is the onset of supersaturation. As a result of the elevated vapor pressure on the surface, molecular diffusion is boosted by the increased vapor concentration gradient, leading to a higher evaporation rate. Consequently, surface temperature drops in response to the enhanced evaporation, which takes heat away from all possible sources (such as air, water, and radiation sources in all available spectral ranges) as the system tries to move toward another equilibrium state. Since saturation pressure is strongly dependent on temperature, the degree of supersaturation will be further lifted up as the surface temperature drops. Eventually supersaturation will increase to reach a new quasi- steady state at which absorption of characteristic radiation (“+” term) can no longer surpass emission (“” term) in Eq. (30). The new quasi-steady supersaturation is assumed to be,

cos θδω Ð ∞ Iλ s¼ 0 I b, λ H λ dλ; ð31Þ 2π

which gives a zero evaporation flux in Eq. (30) for the integration value over the entire spectral range. Note that Iλ here is the excess radiation intensity and the quasi-steady s is independent of the probability constant a21. For diffuse radiation with intensity Iλ coming from above (i.e., hemispher- ical radiation intensity independent of incident angle), the quasi-steady supersaturation is,

enhances evaporation by uplifting the surface vapor mass fraction, m1,s, in Eq. (19). In distilla-tion applications, this mechanism allows enhanced evaporation to take place below the boilingpoint.In Eqs. (26)–(32), (H/Ib) is dependent on temperature but invariant with respect to the evalua-tion basis (wave number 1/λ or frequency ν, or even wavelength λ). To facilitate engineeringanalysis, coefficients for curve-fits of (H/Ib) defined in Eq. (33) are tabulated in Table 6 for λfrom 2.5 μm to the far wing where Hλ approaches zero (see Figure 4, generally >7.25 μm,depending on T). The units for λ and (H/Ib) in Eq. (33) are, respectively, [μm] and [cm2-sr/W].

X H cm2 -sr 6 i ¼ PðiÞ λ μm : ð33Þ Ib W i¼0

2.4.9. Local stability of quasi-steady supersaturation

The quasi-steady supersaturation in Eq. (31) or (32) is in favor of the local stability of thethermodynamic system. This is explained as follows. For a system already at quasi-steadystate under IR characteristic radiation, a perturbation is added to the established supersatura-tion to examine the stability of the system. The perturbation can be either positive or negativewith respect to the quasi-steady supersaturation. For a positively perturbed supersaturation,the net radiation-induced evaporation rate in Eq. (30) will become negative as a result of theslightly increased supersaturation to bring the system back to its original quasi-steady state.

Table 6. Curve-fit coefficients for (H/Ib) in Eq. (33).

118 Distillation - Innovative Applications and Modeling

On the contrary, a negative perturbation for supersaturation results in a positive net radiation- induced evaporation rate to restore the system to its prior unperturbed quasi-steady state. Therefore a locally stable state is established at the quasi-steady supersaturation.

2.5. Materials and methods

The most crucial part in the engineering application of radiation-enhanced evaporation is the selection of the IR radiation source. Since the characteristic radiation is in the mid-IR spectral range, lasers and LEDs designed for this range fit in well for this purpose. However, they are not economically feasible on industrial scales. An alternative way of generating mid- IR radiation is to heat up a Blackbody-like material to a desired temperature such that the peak of its Blackbody-like radiation locates within the spectral range of characteristic radiation. Based on Wien’s displacement law (λmax [μm] T [K] = 2898 [μm-K]), T = 200–300 C corresponds to λmax = 6.12–5.06 μm. At T = 250 C, the corresponding λmax (=5.54 μm) appears to be a preferred choice because it is near the maximums of population distributions in Figure 4. Surface treatment is perhaps one of the most affordable methods to create Blackbody-like surfaces. Applying paints over surfaces can achieve this purpose because paints are usually “black” in the mid-IR spectral range. Anodized aluminum coating, which is commonly prac- ticed in industries to passivate aluminum surfaces, is able to produce a moderately high emittance (~0.85, depending on several factors such as temperature, color, thickness, and roughness) [12] to somewhat resemble Blackbody surfaces. If there is no appearance prefer- ence in the engineering design, black color is generally recommended for surface treatment to mimic the Blackbody emittance. As far as mass and heat transfer analysis is concerned, the temperature at water surface Ts needs to be determined before other thermal variables can be calculated. This can be done by plotting Eq. (25) in spreadsheet to visually determine Ts, as shown in Example 3. Alternatively, a computational method for computer-aided calculations is suggested in Figure 7. The logic behind this method for finding Ts is explained also in the same example.

2.6. Results and discussion

This section guides readers through examples to deal with water vaporization problems in distillation applications. Comments are made following the results of these examples to help readers understand methodologies presented in this chapter.

2.6.1. Example 1—isothermal water under mid-IR radiation

Consider a still lake with surface temperature Ts fixed at 20 C and a temperature gradient that vanishes at the bottom of the lake. Provided that a diffuse mid-IR radiation field with qr,s = 1000 W/m2 is applied to water surface from above, estimate the maximum temperature change from its surface to the bottom due to radiative heating. Assume cloudy sky to skip solar radiation and evaporation flux, m_ ″ ¼ 104 kg=m2 -s. Enhanced Distillation Under Infrared Characteristic Radiation 119 http://dx.doi.org/10.5772/67401

used as means to generate supersaturations instead of as major heat sources. The idea here is to apply the right amount of IR radiation in the right spectral range so that the desired supersat- uration can be achieved in an economical way.

2.6.2. Example 2—economic evaluation

Given that the cost of household electricity is $0.2 USD/kWh (for example in Cambridge, Massachusetts, USA) and the desired evaporation flux is 104 kg/m2-s, evaluate the minimum cost ($USD/Ga) for water distillation at 100 C. In the economic evaluation ignore heat loss/ recovery, sensible heat for water to reach 100 C and costs related to vapor condensation and water collection.

Heat of vaporization at 100 C: 2257 kJ/kg.

kWh kg 3600s ¼ 0:125USD=kg.

2257kJ Cost per kg: $0:2USD hour

958kg 3 Cost per gallon: $0:125USD kg m3 0:003785m Ga ¼ 0:453 USD=Ga.

Note that at room temperatures water density is 4% larger than that at 100 C, giving an adjusted minimum distillation cost $0.47 USD/Ga. The retail price of distilled water at Walmart (brand: Great Value Distilled Water, 1 Gal) is $0.88 USD/Ga. There are several options to reduce the production cost of distilled water: choosing a cheaper energy source, minimizing heat loss while vaporizing water, recovering heat release during vapor condensation, or using a new method for water vaporization such as what is proposed in this chapter.

2.6.3. Example 3—computational methods

Given that the temperature at the top of vapor layer thickness is Te = 30 C and the corresponding relative humidity (RH)e = 0.8 and ignoring radiation effects, calculate the quasi-steady surface temperature Ts at P = 1 atm. For vapor layer thickness L = 1 mm, what is the quasi-steady evaporation flux?

Solution 2.6.3.1. Surface temperature Since radiative heating is ignored, the isothermal approximation is applicable for liquid-water, i.e., h1,o = h1,u = 4.2Ts[ C], and there is no IR induced supersaturation, i.e., (RH)s = 1. In Figure 2 Le for saturated air (Le ≈ 1.19) can be used because of the high relative humidity. From steam tables, Psat,e (Te = 30 C) = 0.0419 atm. To begin with we shall assume a dilute system, in which Cp ≈ 1 kJ/kg-K. The value of m1,e supports this assumption, Enhanced Distillation Under Infrared Characteristic Radiation 121 http://dx.doi.org/10.5772/67401

ð0:8Þð0:0419Þ m1, e ≈ ¼ 0:0211: 1:61 0:61ð0:8Þð0:0419Þ

Eq. (25) gives,

Psat, s 1:61 30 T s ð CÞ ≈ ð0:8 0:0419Þ þ : P 1:19 2501 3:2T s ð CÞ

Two methods are used to obtain Ts.

Method 1: The correct value of Ts can be found by plotting the right hand side (RHS) and lefthand side (LHS) values for Psat,s/P (based on either steam tables or Table 1 for Psat) with respectto guessed Ts in spreadsheet. The results are shown in Figure 8. The LHS curve intersects withthe RHS to give the correct Ts = 27 C.

Method 2: As shown in Figure 7 the value of Ts needs to be guessed to find the correspondingPsat,s. Plugging in the guessed Ts the RHS result is compared with the LHS for Psat,s/P. If furtherguesses are needed, the RHS value of the present guess can be conveniently used as the LHSvalue of the new guess. This guessing method is applicable because the RHS and LHS curvescome across each other at the right Ts as shown in Figure 8.Saturation pressure Psat and temperature Ts can be calculated using formulas for Psat and Tsat inTable 1.

The 4th guess gives a fairly good match between RHS and LHS. For Ts = 27 C, the mass fraction of vapor at surface m1,s is 0.0222, which also supports the dilute assumption. This method seems to be tedious but becomes powerful in computer-aided computations, in which the iteration method can easily be implemented in the code.

2.6.3.2. Evaporation flux

The calculated Ts (=27 C) is quite close to the wet-bulb temperature for the high RH condition in this example. Based on the online RH calculator by National Weather Service Weather Forecast Office (http://www.srh.noaa.gov/epz/?n=wxcalc_rh), the web-based wet-bulb temperature is 27.13 C.

2.6.4. Example 4—enhanced evaporation by supersaturation

Following Example 3, assume that surface supersaturation can be elevated to 20% by mid-IR radiation for the isothermal liquid, and calculate the quasi-steady surface temperature and evaporation flux. Assume radiative heating in the mid-IR range can be neglected, i.e., Tr,s << (Te Ts), in this example (for practical situations see Example 5).

Solution

2.6.4.1. Surface temperature

To approach the right value of Ts Eq. (25) is employed with (RH)s = 1.2 and Tr,s = 0. Table 1 is used to calculate Psat and Tsat at surface. Le is approximated by 1.19 for this high RH system. Based on Method 2 in Example 3 (also shown in Figure 7), surface temperature can be evaluated to give Ts = 24.56 C. The quasi-steady surface temperature is brought down by ~2.5 C as compared to the saturated water surface in Example 3.

By boosting supersaturation to 20%, evaporation mass flux is 70% higher than that (=3.35 105 kg/m2-s) in Example 3. The amount of mass flux may not seem appealing in this high RH Enhanced Distillation Under Infrared Characteristic Radiation 123 http://dx.doi.org/10.5772/67401

example. Nevertheless, through this pure diffusion problem it is shown that supersaturationsignificantly enhances evaporation.

2.6.5. Example 5—engineering application of induced supersaturation for water vaporization

Consider a still indoor pool with uniform water temperature 293.15K and the temperature ofthe ceiling is the same as the ambient at 303.15K. Assume Blackbody for the ceiling and watersurface, and calculate the quasi-steady supersaturation and the relative humidity above vaporlayer. For vapor layer thickness L = 1 mm, compute the evaporation flux and analyze how heatis supplied to liquid-water during the evaporation process. If radiation energy from the ceilingis supplied by electric heating, what is the unit cost for water vaporization based on theelectricity price in Example 2 (i.e., $0.2 USD/kWh)?

Using Table 5 for Hλ, the integration result for s is s = 0.185. A slightly different value of s =0.187 is obtained based on H/Ib curve-fit values from Table 6.In the midst of various sources of experimental uncertainties, the elevated supersaturation caneasily be misidentified as a different thermodynamic variable such as a higher surface temper-ature. It is shown in the next example that, without considering Eq. (32) or (34), increasing Tsby 2 C gives s = 0 to satisfy mass and heat transfer equations at a different evaporation rate.This temperature difference (2 C) is within the accuracy range of K-type thermocouples [13].

2.6.5.2. Relative humidity

The radiation characteristic temperature Tr,s is taken into account to solve for the value of (RH)e.Table 1: for Tavg = 25 C => k = 2.59 102 W/m-K (curve-fit coefficients in Table 2 [5]), and

Water density at 20 C: 998 kg/m3.

Gallon to cubit meter conversion: 0.003785 m3/Ga.

kWh kg 3600s ¼ 0:0253 USD=kg

As compared to Example 2, the unit cost (per gallon) for water vaporization is reduced from $47 cents to $10 cents. In practical engineering applications, the ceiling temperature, which reflects Tbkgd for the radiation source, can be different from the ambient temperature and the production volume can be scaled up by increasing water surface area. Eq. (34) describes general situations for quasi-steady supersaturations induced by background (hemispherical) Blackbody radiation sources. Figure 9 is constructed based on Eq. (34) to give supersaturations for some representative surface temperatures Ts and background Blackbody temperatures Tbkgd. It is seen in Figure 9 that a higher Ts corresponds to a lower quasi-steady s for a fixed Tbkgd, which is the upper limit of Ts to give s = 0. In order to achieve s = 0.2, Tbkgd needs to be higher than Ts by 10.7–13.0 C respectively for Ts = 20–50 C. For a fixed Ts at 20 C, s can be uplifted from 0.2 to 0.6 by increasing Tbkgd from 30.7 to 46.0 C. Note that a recommended Blackbody temperature to induce supersaturation is 250 C as discussed in Section 2.5. Since it is costly to attain such a high temperature for the entire hemispherical surface above water surface on industrial scales, a radiation source with this Enhanced Distillation Under Infrared Characteristic Radiation 125 http://dx.doi.org/10.5772/67401

Following Example 5, with the same ambient temperature, ceiling temperature, and (RH)e (=0.49),assume saturated water for the pool surface, i.e., s = 0 or (RH)s = 1, calculate the correspondingsurface temperature, evaporation flux, and the amount of heat conducted from air to the poolsurface. In this example the effect of characteristic radiation on supersaturation is ignored.

From steam tables, heat of evaporation: hfg (22 C) = 2449 [kJ/kg].

The conduction contribution to Hfg is

dT 30 22 k ¼ 0:0260 ¼ 208 W=m2 : dy s 0:001

The radiation contribution is 49 W/m2. The evaporation flux without supersaturation drops by ~20% as compared to that in Example 5 and the amount of heat conducted/extracted from air also drops by ~20%.

3. Conclusion

For semi-infinite water under mid-IR radiation, the liquid phase is essentially isothermal as a result of the pronounced IR absorption of radiation in liquid-water. When vapor mass fraction is small compared to the air, the dilute approximation can be made and equations for mass and heat transfer can be significantly simplified. Together with these simplified forms for dilute approximations, empirical forms for thermodynamic properties are also presented in this chapter to facilitate engineering analysis.

The situation of supersaturation induced by IR characteristic radiation suggests a potential way

to enhance evaporation below the boiling point. Characteristic radiation applied on the water surface directly drives water molecules out from the surface to cause evaporation. When excess IR radiation is continually applied over the surface, the quasi-steady supersaturation can be reached to enhance evaporation. Since water is nearly isothermal under mid-IR radiation with moderate radiation strength, a significant amount of heat is extracted from the air to supply the latent heat of evaporation. Blackbody-like materials heated to ~250 C can serve as mid-IR radiation sources. Economical Blackbody-like materials include black anodized aluminum surfaces and metal sur- faces painted in black. With supersaturation induced by characteristic radiation in the mid-IR range, this chapter offers an economical way to enhance evaporation in distillation applications.

Acknowledgements

The second author would like to acknowledge the support of the Hermia G. Soo Professorship and NSF Grant 1457128.

Author details

Kuo-Ting Wang1,2*, M. Quinn Brewster1 and Wei-Hsiang Lai2

*Address all correspondence to: calebuiuc@gmail.com

1 Department of Mechanical Science and Engineering, University of Illinois at Urbana-

Distillation Techniques in the Fruit Spirits Production

Nermina Spaho

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66774

Abstract

During the distillation of the fermented fruit mash or juice, ethanol and water are the carriers of a huge number of the other volatile aroma compounds. Unique and distinctive flavour of the final spirits depends on their quantity and quality. Fruit spirits have higher concentration of almost all types of volatile compounds with comparing to other types of distilled spirits. The art of distillation run is to obtain the best balance between congeners present. Two different types of distillation equipment are used for the production of fruit spirits: copper Charentais alembic and batch distillation columns. Although both distil- lation methods are based on the same theoretical principles, a different quantity of the flavour compounds of the final spirits is produced by using different distillation equip- ment. The main difference was shown in different distributions of the methanol, n-pro- panol, higher alcohols and fatty acid esters. Distillation methods need to be adjusted for each fruit spirits regardless to distillation equipment employed because fermented mash of different fruit varieties has a different requirement for distilling. Alembic stills yield better aroma and more characteristic fruit distillates but are slow and require more labour. Column still cleans the distillate giving a decent aroma and higher concentration of alcohol.

Fruit spirits are popular alcohol beverages due to their unique flavour. They are consumed invarious countries all over the world. Very often fruit spirits represent the national drink of thecountry, so the Hungarians are proud on their apricot spirits; French on Calvados; Italians onapple spirits [1]; Greeks on mulberry spirits [2]; Balkan countries [3, 4] and Eastern Europeancountries on plum spirits [5]; and Germans and Swiss on their ‘kirschwasser’ [6]. Althoughfruit spirits could be made from each type of fruit that contains at least a few amounts of sugar,130 Distillation - Innovative Applications and Modeling

either cultured or wild fruit, the most popular fruit spirits are made from plums, cherries, apples, pears, apricots and quinces. The nice, unique and pleasant aroma is common for all of them. The main ingredients of these beverages are water and ethanol, and they account around 99% of the total content of the spirits. Nevertheless, the fruit spirits are not a pure diluted etha- nol; in that case one could not make differences between plum spirits from quince or pear spir- its. Fruit spirits must be recognised on the raw material from which it obtained. Hundreds of different compounds, so-called congeners, have been identified in fruit spirits, present in very low concentration but crucial for the quality of beverages. The composition and concentra- tions of these congeners vary depending on the cultivar used for the production, fermentation procedure, yeast strain used, time of storage of fermented mash before distillations, distilla- tion technique, use of post distillation processes and maturation of spirits. Thus, it seems that the quality of spirit and its identity and character are influenced by a huge number of factors. Some authors favoured raw material as a factor of great influence on character and authentic- ity of fruit spirits [7–9]; others said that fermentation is the most important activities in aroma compound production; another, however, wrote that distillation is a technique that manages the composition of aroma compounds present in the spirits [10–12], whilst some other authors highlighted the ageing of spirits in creating their unique quality [13, 14]. However, the truth is somewhere between of all these views. Nevertheless all researchers are agreed that all phases have to be adequate carried out in order to achieve the fruit spirits premium quality. The production of fruit spirits has a long tradition in Croatia and the other West Balkan coun- tries (Bosnia and Herzegovina, Serbia, Montenegro, Macedonia, Kosovo and Albania). The most popular is plum brandy or Sljivovica although recently; all kinds of fruit are used in spirits production. Traditional production of the fruit spirits involves the use of simple distil- lation pot still (Charentais alembic or French style). In the last decade, the batch distillation columns (German style) are introduced in the production of spirits in small distilleries. The distinctive identity of spirits can be affected by various distillation devices used. Very often the distillation run is left to the skills of distiller, and sometimes they have no experience to govern the distillation, resulting unpleasant and pungent flavour of the fruit spirits obtained, without distinctive identity.

For this reason, this chapter has an aim to give an overview of the basis of distillation process and main characteristics of commonly used distillation techniques in fruit spirits production.

2. Theory of distillation

Simply, distillation is the process in which a liquid is vaporised (turned to steam), recon- densed (turned back into a liquid) and collected in a container. Distillation is a very old separation technology for separating liquid mixtures into their individual components by the application of heat. The basis for the component separation is differences in their boiling points. Mixture of two or more compounds is separated by heating it to a certain temperature and condensing the resulting vapours. The vapour above a boiling mixture becomes richer in more volatile components. Consequently, a boiling mixture becomes richer in less vola- tile components. That means that the original mixture will contain more of the less volatile material. Distillation Techniques in the Fruit Spirits Production 131 http://dx.doi.org/10.5772/66774

2.1. Distillation of binary mixture (ethanol-water)

Spirits mainly consist of the ethanol and water in quite equal portions. Alcohol has a lowerboiling point than water (78.5°C compared to 100°C for water). Depending on the ratio ofalcohol to water, mixture will boil at all temperatures between 78.5 and 100°C. Due to dif-ferences in boiling points, the vapour above the liquid will be richer in alcohol than water atthe any moment of evaporisation. Alcohol-water relationship between gaseous and liquidalcohol-water mixtures is shown in Figure 1. As it can be seen in Figure 1, vapour phases arericher in the ethanol than the liquid, at any given mixture. Assuming, a mixture (A) of 6/94%of ethanol and water is supposed to be separated by distillation. The vapour above the liq-uid in the moment of equilibrium achieved will be about 42% of ethanol (A1). Distilling themixture of 42/58% of ethanol and water (A1) produces a distillate that is about 78% ethanoland 22% water (A2), and further distillation of the liquid mixture (A2) will give a vapour withabout 86% of ethanol (A3). This means that initial alcohol strength of liquid was 6% (w/w),and after three distillations, the strength of liquid was 86% (w/w). Further, distillations willproduce mixtures that are closer to the azeotropic ratio of 95.6/4.4% of ethanol and water. Atthis concentration, the alcohol in the vapour phase is no longer more concentrated than inthe liquid phase, and fractional distillation no longer works. A mixture of this composition iscalled an ‘azeotropic mixture’. An azeotropic mixture itself cannot be separated by ordinarydistillation, and, usually, special methods are required. Generally, a third substance mustbe introduced into the mixture to permit separation by distillation, or some other separa-tion schemes must be used, e.g. distillation under lower pressure not at the atmosphericpressure.Referring to Figure 1, some main remarks could be given. If we put in ratio concentration ofethanol in the vapour to concentration of ethanol in the liquid (that is in this case A1/A), wewill get 42/6 = 7. It means sevenfold increase concentration of alcohol. The next step of distil-lation gives ratio A2/A1, that is 78/42 = 1.9 and finally A3/A2 or 86/78 = 1.1. It is obvious that thehighest strength of ethanol happened when the concentration of ethanol was the lowest in theinitial liquid. Here is about equilibrium ratio (K value) or distribution coefficient. It representsthe ratio of the mole fraction some particular component in the vapour, y-axis to the molefraction in the liquid x-axis. K value is defined by ​y​ ​ K = ​________ ​ ​ x​A ​​​ (1) A

where yA and xA are the mole fractions of component A in the vapour (y) and liquid phases(x). For the more volatile components, the K values are greater than 1, whereas for the lessvolatile components are less than 1. The K value is sometimes called the equilibrium ‘con-stant’, but this is misleading as it depends strongly on temperature and pressure or composi-tion [15].It is important to know how ease or difficult; the two components will be separated from thebinary mixture (e.g. mixture of component A, more volatile component, and B less volatilecomponent). Comparing the K values for these two components, relative volatility (denotedby α) obtained: yA ___ ​ ​ ​K​ ​ α = ​___ ​ xA ___A yB ​ = ​ ​K​ ​​​ (2) ​ ___ xB ​ B132 Distillation - Innovative Applications and Modeling

Relative volatility is a measure of the differences in volatility between two components and hence their boiling points. It indicates how easy or difficult a particular separation will be. Thus, if the rel- ative volatility between two components is equal to 1, separation is not possible by distillation. The larger the value of α, above 1, the greater the degree of separability, i.e. the easier the separation.

The values of α will be less dependent on temperature than the values of K since the K all increases with temperature in a similar manner. In general, relative volatility of a mixture changes with the mixture composition.

2.2. Distillation of multicomponent mixture (fermented mash)

In the production of fruit spirits, the initial material for distillation is fermented mash (or juice) that contains the ethanol and water as main compounds and a huge number of other volatile compounds that have a very large boiling point difference (e.g. acetaldehyde 20.8°C and benzal- dehyde 179°C). These are collectively known as congeners, and they give the spirits authenticity and flavour. Some congeners are desirable in small quantity; others should be removed as more as possible during distillation. It is complicated to measure the relative volatility for each individual component in a multicomponent mixture. There are many reasons for that, and some of them are the following: compositions and concentrations of compounds are changing continuously with time, the aroma compounds are highly dependent on ethanol content in the liquid phase from which they are vaporising and compounds interact with themselves and between each other. Distillation Techniques in the Fruit Spirits Production 133 http://dx.doi.org/10.5772/66774

Distillation is performed with the aim to concentrate ethanol and desirable aroma com-pounds, so the relative volatility for the each individual component (i) is defined with respectto ethanol (E) and denoted by ​ai = ​Ki​ ​/​ ​K​ E​​ ​ (3)

In that sense, all congeners could be separated with respect their α value on the:• compounds with α > 1 (these compounds are more volatile than ethanol)• compounds with α < 1 (these compounds are less volatile than ethanol)• compounds with α = 1 (separation of these compounds from ethanol is not possible)Congeners rarely have a permanent α value greater than 1 or less than 1, due to the congenersthat will distill differently depending on compositions of initial mash, their solubility in theethanol and water, content of ethanol, variation of ethanol content in the vapour during dis-tillation, distillation technique employed and regime of distillations. Some of the importantcongeners that almost ever have α > 1 are acetaldehyde, typical representative of the firstdistillation fraction, or opposite, acetic acid that almost ever has α <1 and distills in the thirdfraction. Thanks to the differences in boiling points of congeners, their different solubility inthe ethanol or water and the variation of ethanol content in the vapour during the distilla-tion of all congeners will distill separately [16]. It is the basis for the separation of unwantedcompounds, or concentration wanted volatile compounds during distillation of fermentedfruit mash. The possibility of the separation volatile compounds enables the distiller to have acontrol over the process of the separation a large group of volatile compounds and ensure theproduction, health and pleasant quality of fruit spirits.

3. The distillation cut

During distillation ran the ethanol and water are the two main components which are actuallycarriers of all other volatile compounds (Figure 2). It could be considered that the ethanol vapourwill carry over the compounds favouring spirits aroma and flavour and therefore the quality.At the very beginning, the high volume of ethanol comes out of the still together with highvolatile compounds. Through the time volume of alcohol is decreased followed by water,and low volatile compounds increased. According to this, the distillate is cut to three cuts orfractions: the head, the heart and the tail. The heads contain higher concentration of low boil-ing point components and mainly contain undesirable compounds. These compounds wouldgive the distillates an unpleasant, strong and sharp flavour. In the first cut, there is a higherconcentration of some toxic compounds, and therefore it must be eliminated. The best partof the run is the middle part of the distillation, the final spirits. It is a distillate rich in ethanolthat is carrying a pleasant and fruity aroma compounds. The heart cut is a very clean tastelacking the sharp bite of the heads. The last cut is the tail fraction, which has to be eliminatedfrom the heart, since it contains unpleasant fatty and oil compounds. In this fraction, the maincarrier is the water. The water is carrying longer molecules, which are usually unpleasant and134 Distillation - Innovative Applications and Modeling

can be identified by the distinctive smell of ‘wet dog’. The tail fractions (with or without head adding) are collected and redistilled, because it contains a relatively high concentration of alcohol and a valuable congeners.

3.1. How to make cuts during distillation run

In order to produce an aromatic, harmonised and pleasant fruit distillate, it is necessary to

know the right time for distillation cut. During the distillation of ethanol and congeners, it is possible to manipulate the separation of volatile compounds, to clean undesirable and to concentrate desirable aroma compounds. Aroma profile of distillates very often depends on the skill of distiller to cut adequately distillation fractions. The head and tail fractions could be cut on the basis of sensory evaluation of distiller. The presence and absence of volatile conge- ners that give a sharp, strong and unpleasant smell to the head fraction can be cut points for the switching to the heart fraction. Also, the tail fraction starts with flavour that gives a faded, dull character to the distillates, and it should not be difficult for the sensory evaluation and separation. Experienced distillers do this very well by smell. Taste and smell still remain the most reliable method of determining when to make a cut.

The second indicator of cut points that can be used is the percent alcohol of the spirits that’s flowing out of the still, especially for the separation of the heart from the tail cut. The etha- nol strength could be the limiting values for the switching from the heart to the tail. This limiting value varies depending on distillation equipment involved, the fruit variety used, the quality of fermented mash, etc. Finally, the third indicator of the cut points that can be used is the temperature of the vapour before its entering to the condenser. Distiller can make the first cut in the run, when the temperature of vapour in the copper pipe reaches approxi- mately 74–76°C. The heart cut from the tail can be made when the temperature of vapour in Distillation Techniques in the Fruit Spirits Production 135 http://dx.doi.org/10.5772/66774

the copper pipe reaches around 87–88°C, and tail distills until temperature reaches 92–93°C,when distillation could be over.Each of above-mentioned manners of distillation cut has a shortcoming, and the best way is touse all of them as guideline for the separation of congeners during distillation.

4. The two main distillation techniques

Distillation may be carried out batchwise or continuously. Nevertheless, for the productionof fruit spirits, batch distillation is used. Two different types of distillation equipment arecommonly used for the production of fruit spirits: copper Charentais alembic (French style)and batch distillation columns (German style). It is important to carry distillations out slowlyregardless the type distillation equipment employed. Fast distillation could lead the develop-ment of hot spots and consequent accelerated thermal degradation of the final spirit.

4.1. Distillation in the Charentais alembic

In the Balkan countries, a copper alembic pot still has been utilised in artisanal distilleries,small commercial and medium-sized distilleries, in the production of fruit and wine brandy.It consists of a copper boiler, a hat, a copper pipe (pipe is not like swan neck) and a condenser(Figure 3). The pot still is usually heated by direct fire (fuelled by firewood or, in recent times,by natural gas). Distillation in alembic pot stills requires multiple distillations (usually dou-ble) to achieve high degree of alcohol. The aim of the first distillation is to exhaust, as muchas possible, alcohol from the fermented mash. Collected distillate is called raw distillate (orlow spirits) with alcohol content around 15–25% (v/v), that depends on how rich in alcohol-fermented mash was. The second stage of distillation is carried out which aimed at intensifi-cation and purification of the alcohol and has to be carried out much more carefully than thefirst one. In the second distillation, raw distillate is distilled with separation of three fractions.The head fraction (or cut) is collected in the amount from 1 to 2% per 100 L of raw spirits. Theamount of head depends on how damaged fermented mash was. If fermented mash waitsfor long time until distillation is carried out, then higher head needs to be separated. Theheads are thrown out because many unwanted and toxic compounds are present. Therefore,it is most important adequately to separate the heads from the hearts than the tails from thehearts. The heart fraction starts coming out at 60 to 70% (v/v) of ethanol (depends on how richin alcohol raw spirits was) and collects until the alcohol decrease to 40–50% (v/v). The excep-tion is Williams pear spirit. In the production of this spirit, the heart fraction needs to be cut atthe lower alcohol degree (below 40%, v/v) due to the ethyl decanoate ester which distills at thebeginning of the tail fraction. This ester is very important for the Williams pear spirits aroma.Research from Spaho et al. [18] showed that distillation cut of the heart fraction from thetail fraction, at 50% (v/v) of ethanol, proved to be better for the sensory impression of plumspirits made from more aromatic plum like Pozegaca and Bilska rana. The opposite rule wasobserved for the Stanley variety (less aromatic plum), where a better quality of brandy wasachieved with a distillation cut at a lower alcohol content (40% v/v ethanol). After the heart136 Distillation - Innovative Applications and Modeling

is separated, the tail fraction distills until the end, actually, until alcohol degree achieved 3 or 5% (v/v). Measuring the alcohol content during distillation is carried out by alcoholmeter. The tail is collected and could be redistilled later or could be saved and added to the next run. During distillation, all variables are needed to keep constant and flow rate to adjust to 15– 25 mL/min.

Figure 3. Traditional copper alembic pot still. The hat plays a role in the reflux because the vapour came in and will partially condense and run back down to the original liquid in the boiler and be redistilled. The flavour of final spirits was influenced by the shape and size of the hat [19].

Obtained heart fraction usually has an alcohol strength of 45–70% (v/v) that is strongly depends on kind and variety of fruit used for the spirits production [20]. Sometimes, in the Balkan countries, plum spirits, so-called Sljivovica, was produced by sin- gle-stage distillation in the alembic pot still. This type of spirits is very aromatic with so many congeners, and some of them are not desirable (Table 1). Sljivovica, produced by single-stage distillation, has had a double higher content of acetic acid and esters, a higher content of higher alcohols and acetaldehyde than Sljivovica produced by double distillations.

Double 60.6 0.36 209.68 3243.0 3264.11 1.03

Table 1. Average content (n = 5) of the main congeners in Sljivovica produced by single- and double-stage distillation [3]. Distillation Techniques in the Fruit Spirits Production 137 http://dx.doi.org/10.5772/66774

Apart from ethanol, a content of methanol was higher in the Sljivovica obtained by double-stage distillation (Table 1). This is because the methanol follows the ethanol during distilla-tion, and it concentrates more, together with ethanol.

4.2. Distillation in the batch distillation column

Batch distillation column style requires just one distillation to achieve high alcohol degree[21, 22]. In single-stage distillation, also these fractions are separated: the head, heart and tail.Distillation column consists of a copper pot still fitted with column with trays and a dephleg-mator (Figure 4). In the fruit spirits production, column usually consists of three ball trays.

At the very beginning of distillation, the vapour mixture of volatile compounds goes fromthe boiler to the dephlegmator. Incoming vapour is partially condensed in the dephlegmator,returning a portion of it in trays. This process is called reflux, and liquid from a dephleg-mator is called phlegm or reflux condensate. The reflux condensate feeds the trays in col-umn. During distillation, the vapour coming up through the column vaporises alcohol fromreflux condensate, leaving more water to keep dripping down to the next lower tray. Duringthis countercurrent contact of vapour and liquid, which happened on each tray, the vapourstream becomes richer in light components, and the liquid stream becomes richer in heavy138 Distillation - Innovative Applications and Modeling

components. At every interface between the liquid layer and the condensed layer, contact is occurring causing greater separation of the compounds present. This process is called rectifi- cation. Consequently, as more trays are used in distillation, a greater concentration of alcohol and lower concentration of congeners are obtained. Some of these congeners are very pleas- ant aroma compounds, and it is not desirable to clean the alcohol too much. So, the rectifica- tion must be run very carefully, getting in mind what aroma compounds we want to have in the distillate [20, 23–25]. That means that sometimes all three trays should be active, and sometimes not, depending on how clean or how flavourful distillate needs to be.

Since the alcohol was cleaning and concentrating at the trays in the column, it starts coming out of the condenser at 70–87% (v/v). The fewer amounts of heads are collected than in alem- bic pot (~0.5 to 1% per 100 L of fermented mash). The head fraction is collected until content of alcohol decreased at 75–55% (v/v). The heart is obtained with approximately 65–78% (v/v) in volume around 5–10 L per 100 kg mash. After the heart is separated, the tail fraction dis- tills until distillate obtained has an alcohol content of approximately 20–30% (v/v). All the above-mentioned alcohol contents varied from run to run and strongly depend on how much alcohol in the fermented mash has.

The main characteristic of a batch distillation column is that concentrations and temperatures are changing with time at any part of the column, so two methods can be carried out [26]: constant reflux ratio (with variable product composition at distillate) or variable reflux (with constant product composition, for one component, at distillate product). It is usually to carry out distillation with constant reflux ratio.

5. Distribution of volatile compounds during distillation by using

different distillation equipment

Although both distillation techniques are performed on the same theoretical basis and in both cases three fractions have been obtained, there are several important differences in the con- tent of ethanol and congeners that are crucial for the flavour of spirits. The first difference is content of alcohol that entails a lot of other differences. For alembic distillation, the alcoholic strength in the heart fraction is significantly lower than alcoholic strength in the heart frac- tion obtained by using distillation column although both distillation techniques recovered the same amount of ethanol in the hart fraction [27]. Congeners are present in very small amounts in fruit spirits but with a large influence on the bouquet and flavour. Distribution of the main congeners during distillation by using different distillation equipment, simple alembic pot and distillation column, was shown in Figure 5.

As it can be seen in Figure 5, the main differences occurred in distribution of methanol, fatty acid esters, n-propanol and isoalcohols. The main reason, for those differences, lies in the fact that those compounds show different behaviours depending on content alcohol in liquid and vapour during distillation. They will distill following their relationship with alcohol rather than their boiling point. Distillation Techniques in the Fruit Spirits Production 139 http://dx.doi.org/10.5772/66774

Figure 5. Distribution of main volatile compounds by using different distillation equipment: full line, alembic distillation;dashed line, column distillation and *, shows the cut where higher component is accumulated (this figure is createdthanks to results of the authors) [10, 12, 18, 20, 21, 27–33].

Methanol is often the most concentrated compounds in fruit spirits [2, 8, 12, 18, 34]. Methanolis not a by-product of alcohol fermentation but is released very intensively during this pro-cess. The methanol was produced during the processing and storage of fermented mash viathe effects of enzymes on pectin in the cell wall. Actually, methanol is formed from the deme-thoxylation of the esterified methoxyl groups in pectin.

It is characteristic to fruit brandies, significantly higher than in cereal distillates [34]. Its pres-ence in the spirits is proof of natural origin of fruit spirits because the pectin is a natural con-stituent of fruits. Concentration of methanol is dependent mainly on the applied technique ofthe fruit treatment and the distillation and second from the fruit kind and variety.There are different views on methanol impact to flavour of distillates. Such, Ribéreau-Gayon[35], considered the methanol imparts a cooked cabbage odour in spirits, with a threshold of1200 mg/l. Claus and Berglund [21] wrote that methanol is considered to be a positive flavourconstituent in distilled spirits. Nevertheless, most researchers say methanol is colourless vola-tile compounds with a mild or bland odour and does not affect the flavour of distillates [10,32, 36, 37]. However, it is one of the most important compounds to control in the spirits due itsdangerous effect to human health. In some quantities, the methanol can be dangerous becauseit is metabolised to formaldehyde and formic acid, which is primarily responsible for most ofthe toxic effects of methanol [38]. Since it is toxic to humans, the maximum level of methanolis fixed by EU Regulations No. 110/2008. According to these regulations, the concentration ofmethanol in fruit spirits should not exceed to 12 g/L alcohol 100% (v/v).140 Distillation - Innovative Applications and Modeling

The boiling point of methanol is 64.7°C, and it is completely soluble in water. Considering methanol contents in the distillates obtained by different distillation techniques the results reported by several authors are vary. Methanol appears in almost equal concentration in all fractions of distillation due to the formation of azeotropic mixtures [39, 40]. It is really dif- ficult to separate the methanol from the ethanol-water mixture. When low alcohol mixture (like fruit-fermented mash) is distilled in simple pot still, methanol will go out following his solubility in water rather than his boiling point. Methanol is highly soluble in water, there- fore, methanol will distill more at the end of distillations, when vapours are richer in water. That means that methanol will accumulate more in the tail fraction [7, 32],during distillation in alembic pot still as it showed in Figure 6.

When high alcohol mixture distills, methanol will evaporate following his boiling point and will be present in the first fraction of the distillation in higher concentration. It appears mainly in the head fractions when distillation column was used [21]. Results of Cortes et al. [32] showed the concentration of the methanol was seven times higher in the case of indus- trial distillation (means higher concentrates and cleanses of ethanol) than the concentration of methanol in the distillates obtained by simple pot still. The opposite results are given by Arrieta-Garay [20]; there is no difference in methanol content depending on distillation system employed (alembic pot still or packed column distillations), whilst Leaute [16] and Garcia-Llobodanin et al. [27] reported that methanol content was higher in alembic distillates than in the column distillates. The higher alcohols are quantitatively the largest group of the aroma volatile compounds in the distilled alcoholic drinks [32, 41]. They are also called fusel oil although they are not Distillation Techniques in the Fruit Spirits Production 141 http://dx.doi.org/10.5772/66774

oils. It is due to form oil blotches in low alcoholic liquids because they are partially soluble inwater. Higher alcohols are formed during the fermentation process and are considered as by-product of alcohol fermentation. They are produced by yeast during alcoholic fermentation,through the conversion of the branched chain amino acids present in the medium.The chemical classes of higher alcohols include numerous alcohols. The largest share in thehigher alcohol group was amylic alcohols, 2-methyl-1-butanol (active amyl alcohol), 3-methyl-1-butanol (isoamyl alcohol), 2-methyl-1-propanol (isobutyl) and 1-propanol, which are in thehighest concentration present in plum brandy [18]. Very high content of 1-propanol may bean indicator for the spoilage of fruit mash.The quantities of the other higher alcohols were very low. The shares of 1-hexanol, 1-butanol,1-pentanol and 2-butanol were less than 5% of the total amount of the higher alcohols [18].The compounds 1-butanol and 1-hexanol are formed during alcoholic fermentation by thehydrolysis of the corresponding acetates.The content of 2-butanol is usually associated with a low quality of raw materials and isrelated to bacterial action during fermentation. Its presence negatively influences to flavour.1-Hexanol is an alcohol originating only from raw material [2]. The level of 1-hexanol is con-sidered the sensory relevance especially in the apple ciders and associated with a grassy scentin distillates. But, when it is present above 100 mg/L a.a. then 1-Hexanol is responsible for thevery intensive grassy flavour and distillates is unpleasant both in aroma and taste. It is esti-mated that the presence of 1-hexanol in the above-mentioned concentrations imparts to winesand distillates fruity, liquorice and even a toothpaste-flavour profile [42].2-Phenyl-ethanol is an aromatic alcohol and has a rose-like odour. It contributes to pleasantflavour of fruit distillates due its very low odour threshold. Bacteria, fungi and yeasts maysynthesise 2-phenyl-ethanol using L-phenylalanine as a substrate, which allows this metabo-lite to be deemed as a potent genotypic marker for grape marc spirits [43].2-Methyl-butanol and 3-methyl-butahnol are the most abundant minor components of spiritssynthesised by yeast. In trace amounts in fruit spirits, there are also trans-3-hexenol, cis-3-hexenoland trans-2-hexenol, 1-octanol, 3-ethoxy-1-propanol allyl and benzyl, alcohol which are morecharacteristic for stone fruit spirits.Higher alcohols make an important contribution to the aroma profile of distillates. They areresponsible for the pleasant flavour and give an essential character of fruit distillates justwhen they are present in smaller quantities. However, high amounts can affect the distillateflavour, giving a strong, pungent smell and taste [2, 32]. Total higher alcohol concentrations,higher than 3500 mg/L (a.a.), are accepted as being an indicator of poor quality [43].The level of higher alcohol in fruit spirits is influenced by fruit variety, fermentation condi-tions, employed distillation and distillation equipment.

Higher alcohols have boiling points lower than 200°C and are alcohol soluble and partiallywater soluble. During distillation of low alcohol mixture, they will distill when the vapouris rich in alcohol (they want to escape from the water in the mash, due to their low watersolubility). It means they will appear mainly in the head fraction although they have high142 Distillation - Innovative Applications and Modeling

boiling point. When distilling mixture has higher concentration of alcohol (higher than 40% (v/v) [44]), higher alcohol will distill following the boiling points, and their concentration will increase as the distillation process progresses. This explains why distillates in the col- umn showed higher concentration of higher alcohol in the tail [21] and distillates in pot still (Figure 6) showed higher concentration of higher alcohol in the head [18, 40].

Higher concentration of this important flavour compounds is observed in the distillates

obtained in the distillation column still than in the distillates obtained in the alembic pot still [27, 40, 43].

Esters are formed during alcoholic fermentation via yeast metabolism and qualitatively pres- ent the major class of flavour compounds in distillates because they have low sensory thresh- old value. Esters, generally, are associated with a pleasant, fruity and flowery aroma. Their contribution to flavour is strongly influenced by their concentration. Ethyl acetate is the major ester present in distilled alcoholic beverages. In small quantities, ethyl acetate contributes to the pleasant smell of distillates giving them a fruit character. In large amounts, it contributes to a sharp smell and gives a UHO tone (glue smell) of flavour. Ethyl acetate perception threshold of 180 g/hl a.a. gives to the spirits an acidic character [2]. High concentrations of ethyl acetate are indicative of prolonged storage of the raw material and probable acetic bacteria spoilage but could be also influenced by the distillation process. Ethyl acetate in fruit spirits constitutes even more than 80% of all the esters [18]. The impor- tance of ethyl acetate is such that the ratio of total esters and ethyl acetate is used as indicator of quality of spirits. The higher this ratio, the higher the quality of the final product. Boiling point of ethyl acetate is 77.1°C, and it distills mainly in head fraction in both distillation tech- niques used. Distillates obtained in the alembic pot still showed a higher amount of ethyl acetate in comparing with distillates obtained with distillation in distillation column [16, 33], whilst some results [27] showed the higher concentration of ethyl acetate in distillate obtained by using packed distillation column.

Esters of acetic acid and higher alcohols such as isoamyl acetate, isobutyl acetate and 2-phenyle- thyl acetate are presence in relatively significantly amount in all fruit distillates. They are mostly responsible for the flowery and fruity aroma of the distillates. Isoamyl acetate is associated with odour and flavour of bananas, whilst isobutyl acetate is more common to raspberry flavour. Esters C6–C12 are slightly higher in packed column distillates than alembic distillates [45].

Ethyl lactate is considered to give the distillates a buttery flavour and smell of rancid butter, with a perception threshold of 250 mg/l. Its presence can be linked to a malolactic fermen- tation, which is considered spoiled. In low concentration, lower than 154 mg/L [19], being favourable, stabilise the odour and smoothens the firm character of certain substances [2]. Ethyl lactate is associated with tail fraction of the distillate [18]. The concentration of ethyl lactate was higher in the distillates obtained by using alembic pot still than column. It comes from both the double distillation technique and the malolactic fermentation [16]. 2-Phenylethyl acetate is acetate with rose odour. Although it has a high boiling point, it distills in all distilled fractions due to its partial solubility in water. Rodríguez Madrera and Mangas Alonso [10] report that 2-phenylethyl acetate distills mainly in head fractions. Distillation Techniques in the Fruit Spirits Production 143 http://dx.doi.org/10.5772/66774

Ethyl esters from middle-chain fatty acids (hexanoic, octanoic, decanoic and dodecanoic)are compounds of particular interest in fermented beverages and spirits on account of con-tributing fruity and flowery smells and their relatively high levels [47]. They are producedduring the raw material fermentation. Beyond these, ethyl hexanoate is the most abundantof all middle-chain fatty acid esters. Hexanoate (ethyl caproate) supplies an aroma of fruit(banana, green apple, melon, etc.), and, so, its presence is beneficial for the spirit. Ethyloctanoate (ethyl caprylate) is more pungent and less fragrant, decanoate (caprate) is lessintensive and gives fatty tones and dodecanoate (laurate) is less aromatic and has a waxycandle-like odour [19]. Despite high boiling point of fatty acid esters, they are distilled inthe first fractions during pot still distillation due to their better solubility in ethanol thanwater [16]. During column distillation fatty acid esters are accumulated in tail fractions.There are higher amounts of these fatty acid esters in alembic distillate than in columndistillate.

Ethyl esters of long-chain fatty acids are important just when they are present in higher con-centration. Then, they may contribute to odours giving to spirits a candle wax and stearintone. Esters from this group are also poorly soluble in water, so their elevated concentra-tions may cause turbidity and flocculation and therefore be important factors of distillateinstability [48].

The major carbonyl compound in distillates is acetaldehyde, a direct alcoholic fermentation

by-product. Moreover, significant acetaldehyde concentration may be formed by oxidation ofethanol by acetic acid bacteria in the presence of oxygen. That is one of the reasons why distil-lation should be carried out as soon as possible after fermentation is finished. The content ofacetaldehyde is not influenced by a variety of raw material [48]; it is influenced by the strainsof yeasts [49], by fermentation process and manner of distillation cut.

It has a distinctive aroma characteristic, and when it presents in higher concentration, it hasa sensorial negative impact. Its importance derives not just from the pungent smell it bringsalong, as well as its chemical reactivity. This makes it a harmful component for the consumers.It is usually associated with intoxication and ‘hangover’ symptoms such as nausea, vomiting,restlessness, sweating, confusion, decrease in blood pressure, higher heart rate and headache[50]. Some authors [33, 51] established 120 g/hl a.a. of total aldehydes (mainly acetaldehyde)as limiting values before they significantly affect the aroma of the spirit.In low concentration odour of acetaldehydes, resemble hazelnuts, cherry and overripe apples.It has a relatively low odour perception threshold. As acetaldehyde has a low boiling point,its largest concentration is distilled into the head portion of the distillate (Figure 6). It is com-pletely soluble in both water and ethanol. The lower concentration of acetaldehyde is reportedin distillates obtained in alembic pot still than in column distillation [16].

Acetaldehyde accounts for c. 90% (v/v) of the total aldehyde content in spirits. Other alde-hydes, important for the quality of spirits, are isobutyraldehyde, 2-propenal (acrolein), and3-hydroxy-2-butanone (acetoin) 2,3-butanedione (diacetyl). The presence of aromatic defects144 Distillation - Innovative Applications and Modeling

in spirits is related to metabolites such as acrolein (highly toxic substance) and diacetyl. Acetoin is related to carbohydrate metabolism and can be formed by enzymatic condensation of two acetaldehyde molecules or from diacetyl reduction. Acetals are products of condensa- tion of aliphatic aldehydes and alcohols. Acetals contribute to aroma of numerous alcoholic beverages obtained from fruits. They impart a delicate pleasant taste and bouquet to alcoholic beverages. The sum of acetaldehyde + acetal, defined as total acetaldehyde, shows rather low values that confirms a mostly correct technological process, with a regular fermentation without oxidative events. Acetaldehyde and other short-chain aliphatic aldehydes (propanal, butanal, pentanal, (E)-2- pentenal, 2-methyl-1-butanal and 3-methyl-1-butanal) have pungent, rancid and fatty odour, which may increase the tang of distilled beverages. In general, aldehydes with up to eight carbon atoms, such as acetaldehyde, formaldehyde, acrolein, benzaldehyde and furfural, have penetrating odours, generally sickening, which are considered undesirable in spirits [52]. Long-chain aldehydes are characterised by pleasant aroma. Most of them are present at levels below their individual perception thresholds [53]. Benzaldehyde is one specific aldehyde especially important for the spirits made from stone fruits like plum, cherry and apricot. Benzaldehyde is formed by hydrolysis of amygdaline present in fruit seeds and stones. It contributes to bitter almond, marzipan, cherry flavour in spirits. Benzaldehyde and benzyl alcohol are present in spirits in much higher concentrations if the mash is fermented with stones. It is not desirable in higher amount but in small amount contributes to complexity of flavour. Benzaldehyde is a high boiling point compound and distills mainly in tail regardless of distillation technique employed. Furfural is aldehyde formed during distillation due to dehydration of residual sugars (pen- toses) caused by heating in acid conditions and/or Maillard reaction. Furfural may be formed as a result of oxidation of ascorbic acid [54]. Thus, furfural is a normal constituent of fruit dis- tillates and can be used as an indicator of distillate naturalness. Its sensor effect to the distillate can be seen through its influence to the distillate aroma that is increased by the smell of bitter almond, whilst the increased furfural concentrations may contribute to the ‘hotness’ of spirits. The furfural quantity in the dried fruit distillate is naturally higher because the raw material itself has already experienced one heating process where pentose and pentosane dehydration and furfural formation occurred [55].

Furfural is a compound that is soluble in water and for this reason distills mainly in the tail fraction regardless of distillation technique employed. The higher concentration of furfural is ascribed to longer duration of distillation [56]. Its content is higher in spirits obtained by using alembic pot in comparison with the column distillation [48]. The probable reason for this is heating the alembic during double stage of distillation by direct flame.

Acetic acid accounts for more than 90% (v/v) of the total acidity in spirits. Acetic acid is a by- product of alcohol fermentation. It can be formed during the catabolism of sugar in the pres- ence of oxygen and the yeast Saccharomyces cerevisiae. Acetic acid is produced by oxidation of acetaldehyde, and its content in alcoholic beverages mainly depends on the yeast strain applied. High level of acetic acid in the fermented mash is associated with contamination with Distillation Techniques in the Fruit Spirits Production 145 http://dx.doi.org/10.5772/66774

acetic bacteria. In that case, the content of acetic acid is increased, and ethanol is decreased.This is owing to the conversion of the alcohol in acetic acid. A high level of acetaldehydedirectly determined the acetic acid concentration in the analysed plum brandies [5].

Acetic acid is an important compound for the quality of spirits. Acetic acid has a distinctivesour taste and pungent smell, but the low concentration of acetic acid is desirable since lowbeverage acidity is an indicator of better quality and consumer acceptance [52]. In Figure 6, itcan be seen that acetic acid is present in tail. It was mainly found in the last fractions [10, 16],owing to its high boiling point (117°C) although Rodríguez-Bencomo et al. [33] observed thatit could be more concentrated in the head when using variable internal column reflux.

Other volatile acids important for the distillates are present in much lower quantities than ace-tic acid. Those are carboxylic acids and fatty acids like formic, propionic, butyric, isobutyric,caproic, undecanoic, myristic, valeric, isovaleric, 2-methylbutyric and pelargonic acids [51].Fatty acids are known to play an important role in the sensory quality of beverages. They con-tribute to flavour as precursors of volatile compounds. They built esters with higher alcohols.

Caprylic, capric and lauric acids are, second to acetic acid, the most abundant free fatty acids;they are produced by yeast-mediated metabolism of carbohydrates. Short-chain free fattyacids have unpleasant odours similar to rancid butter and putrid cheese, and their presence athigh levels is an indicator of poor quality fruit mash.

Hydrocyanic acid (HCN) initially occurs in bound form in the stones of the fruits and isreleased through enzymes during the maturation process and after the harvest. Hydrocyanicacid is formed by enzymatic hydrolysis of cyanogenic glycosides (such as amygdaline) dur-ing alcoholic fermentation. Spontaneous fermentation of fruit pulp resulted in much higheramounts of HCN in the spirits obtained in relation to the contents observed in the distillatesfrom the mashes fermented with the addition of S. bayanus wine yeast. In the majority of fer-mented mashes, the maximum dynamics of HCN liberation was recorded on the first day ofthe process [57].

During hydrolysis of cyanogenic glycosides, benzaldehyde also occurred. It means that oneproduct of hydrolysis is desirable (consumers often desire the typical ‘bitter almond’), andthe other be accompanied by detrimental influences and health risks [58]. It is particularlyimportant not to largely crush the stone during preparation of stone fruits mashes for thefermentation. Another important item is that distiller should not be carried out distillationof fermented mash with stone in the pot. Investigation of Schehl et al. [58] showed that thepresence or absence of stones in the mashes cannot be used as a general quality criterion.Their data provide strong evidence that the preference bitter almond flavour of spirits or thespirit, without this flavour, will remain a matter of personal taste. The boiling point of HCNis 25.7°C so it seems to be distilled in the first fraction.

Ethyl carbamate (EC) or urethane occurs naturally in many fermented foods and bever-ages. Possible routes of EC formation in alcoholic beverages are associated with the reaction146 Distillation - Innovative Applications and Modeling

between ethanol and nitrogen precursors, such as urea, carbamyl phosphate (e.g. fermented beverages) and cyanide (e.g. spirits) [59]. Cyanate is probably the ultimate precursor in most cases, reacting with ethanol to form the carbamate ester. Ethyl carbamate forms in stone fruit distillation, when exposed to light, from the natural precursors of fruit mash and ethyl alcohol. It is a potentially carcinogenic substance found in significant amounts in distilled fermented beverages, particularly in stone fruit spirits. The EC levels increase with product overheating during the distillation of spirits, especially in the distillation of some beverages rich in cyanogenic glycosides, such as amygdalin in some stone fruit brandies. Current EU legislation determines a maximum EC amount of 150 μg/l in distilled beverages.

There is high variability in ethyl carbamate content. Ethyl carbamate distills more in head and tail fractions than in the heart [59], while Alcarde et al. [60] reported that content of ethyl carbamate is increased during distillation process.

6. Alembic pot still versus column still

One of the most relevant steps in elaboration of spirits is distillation process. Distillation process can be used to correct possible mistakes that have occurred during the previous pro- cessing of the raw material. In addition, inadequate distillation can cause many defects that are difficult to eliminate by the following technological processes. During the distillation, heat facilitates the fitting of volatile compounds into resulting spirits. For the production of fruit spirits, alembic pot still and batch distillation column are the most suitable because spirits will retain the decent fruit aroma and flavour. Volatile compounds will distill differ- ently depending on the distillation equipment used although, in accordance with results of Cortes et al. [32], for most of the compounds, there were no difference in concentration regarding the distillation equipment used. However, the concentrations of volatile com- pounds were influenced by processing and storage of raw material more than distillation equipment used. Alembic stills yield better aroma that comes from fruit, the so-called primary flavour [12]. The alembic pot still produces distillates that retain the character and personality of their source ingredients. This method is slow and requires more labour, but the usage of simple copper still was preferred by several authors [16, 40]. Also, results of García-Llobodanin et al. [61] showed the distillation of pear wine with less in copper alembic leads to a better quality product. Higher concentration of alcohol and higher separation of other volatile compounds were achieved during distillation in batch column still, giving a decent aroma of distillates. The greater yield is obtained in recovered ethanol, allowing an increased productivity by means of column distillation. This type of distillation is more effective. Nevertheless, the column- distilled spirits contained four times more esters, 20% more higher alcohols, 40% less acetal- dehyde and 10% less methanol than alembic spirits [27]. Some results referred that distillates made by using a distillation column had higher sensory acceptance than distillates made in alembic pot [4, 12]. Opposite results were showed by Alcarde et al. [52]. According to these Distillation Techniques in the Fruit Spirits Production 147 http://dx.doi.org/10.5772/66774

authors a sensory acceptance of cleaner fruit spirits (spirits with lower content of esters,aldehydes, higher alcohols, and methanol) was higher. The art of distillation run is to obtainthe best balance between congeners present.

Also, less aromatic fruit varieties can be used to produce distillates with aromatic character-istics similar to more aromatic variety if a suitable distillation process in distillation columnis used.According to Matias-Guiu et al. [11], the traditional distillation with an alembic pot still allowslimited intervention during the distillation process (only the heating power in the boiler canbe manipulated) to modify the composition of the distillate. A more flexible system is thebatch distillation column (in which the reflux rate can be varied in a wide range). In the sametime, the other investigation [27] showed that the process with batch distillation column ismuch less reproducible than alembic distillation.

Claus and Berglund [21] are observed that distillates produced in the alembic pot still areusually stored in wood for many years (e.g. Cognac and Whisky), whereas the distillatesproduced in the distillation column are stored in the glass and consumed as clear spirits. Iconsider that raw material rather determinates whether distillates will be stored in wood ornot. The author of this chapter considers the way of ageing that is determinates by raw mate-rial used rather than the distillation apparatus. In fruit spirits long ageing would mark theprimary flavour of fruit. If distiller produced a distinctive flavour of some fruit, regardlessof distillation apparatus used, it should protect the pure fruity note, not to give the distil-lates a strong and too much complex flavour gained during maturation in wood (quaternaryflavour). If aromatic fruit spirits need to be stored in wood, then it should be just for a whilsthow they would retain a fruity touch.

7. Conclusion

The choice of distillation technique using either pot still or distillation column is depen-dent mainly of the consumers’ desire for the typical and individual flavour and style ofthe particular fruit spirits. In that sense, distillation method should to be adjusted for eachfruit type and variety. Production of various kinds of fruit spirits requires an individualapproach based on the application of knowledge and understanding the processing of desir-able qualities of the spirits. Adequate managing of distillation technique enables productionof the unique product.

Author details

Nermina Spaho

Address all correspondence to: n.spaho@ppf.unsa.ba

University of Sarajevo, Faculty of Agriculture and Food Sciences, Bosnia and Herzegovina148 Distillation - Innovative Applications and Modeling

[29] Spaho N, Alihodžić A, Begić-Akagić A, Blesić M. Content of methanol in the apple pom- ace distillates. Works of the Faculty of Agricultural and Food Sciences University of Sarajevo. 2010;LV:201–211.

ration of the certain volatiles during plum brandy distillation. In: Proceedings of the 24th International Scientific-Expert-Conference of Agriculture and Food Industry; 25–28 September 2013; Sarajevo, Bosnia and Herzegovina. pp. 204–208.

C. C. Fereira, E. C. Costa, D. A. R. de Castro,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66759

Abstract This work aims to investigate the fractional distillation of organic liquid products (OLP) obtained by catalytic cracking of palm oil (Elaeis guineensis Jacq.) at 450°C, 1.0 atm, with 5, 10, and 15% (wt) Na2CO3, using a stirred tank reactor of 143 L. The fractional distil‐ lations of OLP were carried out in laboratory scale with and without reflux using col‐ umns of different heights, and a pilot‐packed distillation column with internal reflux. OLP and distillation fractions (gasoline, kerosene, light diesel, and heavy diesel) were physicochemically characterized for density, kinematic viscosity, acid value, saponi‐ fication value, refractive index, flash point, and copper strip corrosion. The OLP and light diesel fractions were analyzed by Fourier transform infrared spectroscopy (FT‐IR) and gas chromatography‐mass spectrometry (GC‐MS). For the experiments in labora‐ tory scale, the yields of distillates decrease along with column height, with and without reflux, while those of bottoms products increase. The yields of distillates and gas increase with increasing Na2CO3 content, while those of bottoms products decrease. The densities of gasoline, kerosene, and light diesel produced in laboratory scale with reflux superpose exactly those of kerosene, light diesel, and heavy diesel produced in laboratory scale without reflux. The kinematic viscosity decreases with increasing column height for the experiments in laboratory scale. The acid values of distillation fractions decrease along with the column height for the experiments with and without reflux. The FT‐IR of distil‐ lation fractions in pilot and laboratory scales identified the presence of aliphatic hydro‐ carbons and oxygenates. The GC‐MS analysis identified OLP composition of 92.84% (area) hydrocarbons and 7.16% (area) oxygenates. The light diesel fraction contains 100% hydrocarbons with an acid value of 0.34 mg KOH/g, proving the technical feasibility of OLP de‐acidification by the fractional distillation process.

Pyrolysis and/or catalytic cracking is one of the most promising processes to convert triacyl‐ glycerides (TAGs), the major compounds of vegetable oils and animal fats [1, 2], into liquid biofuels [3], and the literature reports several studies on the subject [3–47]. Both processes have the objective of obtaining hydrocarbons for use as fuels [3, 4, 6–24, 28–37]. However, the chemical composition of organic liquid products (OLP) shows a significant difference because of the complex cracking mechanism of TAGs [4, 5, 10, 19, 25–27]. Besides the type of cracking mode (thermal cracking and thermal catalytic cracking), other factors that significantly affect the liquid fuel composition are the characteristics of raw material, reaction temperature, resi‐ dence time, mode of operation (fluidized bed reactor, sludge bed reactor, etc.), and the pres‐ ence of water in the raw material and/or in the catalyst [6–11, 14, 15, 19, 21–24, 28–30].

One of the advantages of catalytic cracking of oils, fats, greases, and fatty acid mixtures is the possibility of using low‐quality lipid‐based materials [6, 7, 20, 21–24, 28–35, 41] and the com‐ positional similarities of OLP to fossil fuels [3, 6–8, 10, 21–24]. The OLP obtained by catalytic cracking presents lower amounts of carboxylic acids compared to pyrolysis, because of the catalytic activity in the secondary cracking step, where the carboxylic acids are broken up to form hydrocarbons [10], as reported elsewhere [21–23, 30]. The OLP can not only be stored and transported, but can also be refined and/or upgraded by applying physical (filtration, decantation, and centrifugation) and thermal separation processes (distillation, liquid‐liquid extraction, and adsorption) to produce high‐quality green fuel‐like fractions with the poten‐ tial to substitute partially fossil fuels [6, 11, 16, 21–23, 40, 44]. The disadvantages and/or drawbacks of OLP obtained by pyrolysis and/or catalytic cracking of oils, fats, greases, and fatty acid mixtures are the high acid value [8, 11, 14, 19, 22, 45, 46] and high concentrations of olefins, making OLP a corrosive and unstable fuel [9, 21]. To increase the yield of OLP and reduce undesired reaction products, as well as the content of oxygenate compounds, a wide variety of catalysts have been tested in catalytic cracking, particularly zeolites [6, 7, 10, 12, 13, 15–18, 21, 22, 28–39]. However, OLP obtained by catalytic cracking using zeolites and mesoporous catalysts still has a high carboxylic acid content [7, 14, 15, 45].

In this context, studies have been investigating strategies to minimize the high acid values and high concentration of olefins in OLP obtained by catalytic cracking of oils, fats, greases, and fatty acid mixtures, including the application of cheap alkali catalysts such as Na2CO3 to reduce the acid value of liquid biofuels [7, 21, 23, 24, 30, 47, 51–55]. OLP with lower acid val‐ ues makes it possible to apply physical (filtration, decantation, sedimentation, and centrifuga‐ tion) [53–55], chemical (neutralization) [53–55], and thermal separation processes (distillation, Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 155 http://dx.doi.org/10.5772/66759

fuels [21–24, 44, 53–55]. In the last few years, processes have been proposed to remove and/orrecover oxygenate compounds from biomass‐derived bio‐oils including molecular distillationto separate water and carboxylic acids from pyrolysis bio‐oils [56–58], fractional distillation toisolate/enrich chemicals and improve the quality of bio‐oil [59–64], and liquid‐liquid extrac‐tion using organic solvents and water to recover oxygenate compounds of bio‐oils [40, 65].Non‐conventional separation methods using aqueous salt solutions for phase separation ofbio‐oils are also applied [66]. Furthermore, the literature reports several studies upon fraction‐ation of OLP by single‐stage and multistage distillation to obtain hydrocarbon‐like fuels in thetemperature boiling point range of gasoline, kerosene, and diesel‐like fractions [6, 7, 11, 14,15, 21–24, 30, 35, 37, 39, 41, 46–55]. However, until now only a few studies have investigatedsystematically the effect of column height on the chemical composition of OLP [6, 7, 47], butno systematic study has investigated the effect of column height, reflux ratio, and OLP com‐position on the physicochemical properties of the distillation fraction of OLP.

This work aims to investigate the effect of column height, reflux rate, and OLP compositionon the physicochemical properties of distillation fractions and de‐acidification of OLP by frac‐tional distillation using laboratory columns of different heights and a pilot‐packed distillationcolumn with internal reflux.

2. Materials and methods

2.1. Materials

OLP was obtained by catalytic cracking of crude palm oil (Elaeis guineensis Jacq.) at 450°C,1.0 atm, with 15% (wt) Na2CO3 in a stirred tank slurry reactor of 143 L, operating in batchmode, as described in a similar study reported elsewhere [21].

The fractional distillation of OLP with reflux was performed by using an experimental appa‐ ratus similar to that described by Mota et al. [21]. The distillation apparatus had a thermostati‐ cally controlled electrical heating blanket of 480 W (Fisaton, Model: 202E, Class: 300), and a 500 mL round bottom, three neck borosilicate‐glass flask with outer joints, and side joints angled at 20°, 24/40. The side joints used to insert a long thin thermocouple of a digital thermometer and the other used to collect samples, the center joint, 24/40, were connected to a distillation column (Vigreux) of different heights (L1 = 10 cm, L2 = 30 cm, L3 = 50 cm). The borosilicate‐glass distillation columns (Vigreux) with bottom inner and top outer joints 24/40 were connected to an inverted Y‐type glass support, the left side bottom inner joint 24/40 was connected to the dis‐ tillation column top outer joint 24/40, and the right side bottom inner joint 24/40was connected to the 250 mL glass separator funnel top outer joint 24/40. The center top outer joint 24/40 was connected to the bottom inner joint 24/40 of a Liebig glass‐borosilicate condenser. The right side of the inverted Y‐type glass support had a Teflon valve that made it possible to drip only a part and/or fraction of liquid condensates into the glass separator funnel, thus creating a reflux rate. A thermocouple connected to the top outer joint 7/25 of the left side of the inverted Y‐type glass support made it possible to measure the vapor temperature at the top of the borosilicate‐glass distillation columns (Vigreux). A cryostat bath (VWR Scientific, Model/Series: 913174) provided cold water at 15°C to the Liebig glass‐borosilicate condenser. The 500 mL round bottom boro‐ silicate‐glass flask and the distillation column (Vigreux) were insulated with glass wool and aluminum foil sheet to avoid heat losses. Initially, approximately 300 g of OLP was weighed, the heating system was switched on, and the distillation time and temperature were recorded. From the time the vapor phase started to condensate, the Teflon valve was regulated to a reflux rate of two drops per second. The mass of distillation fractions (gasoline, kerosene, light and heavy diesel‐like fuels) was recorded and weighed. The distillation fractions were submitted to the pretreatment of decantation to separate the aqueous and organic (OLP) phases.

(DN 25). The 50 L round borosilicate‐glass vessel and the distillation column were insulatedwith glass wool and aluminum foil sheet to avoid heat losses. Initially, approximately 9.50 kg ofOLP was weighed and introduced inside the distillation vessel and the electrical heating systemswitched on for a heating rate of 2°C/min, being the distillation time and temperature recorded.Afterwards, the freshwater cooling system valve was opened. From the time the vapor phasestarted to condensate, the regulating valve between the reflux divider and the product coolerwas open. The mass of distillation fractions (gasoline, kerosene, and light diesel‐like fuels) wasrecorded and weighed. The distillation fractions were submitted to the pretreatment of decanta‐tion to separate the aqueous and organic (OLP) phases.

3.2. Catalytic cracking of CPO

The process conditions, material balance, and yields of reaction products (OLP, coke, gas, and H2O) obtained by catalytic cracking of CPO at 450°C and 1.0 atm, with 15% (wt) Na2CO3, are shown in Table 2. The obtained OLP yield was lower, but in accordance with similar studies reported in the literature [21–24, 30]. The gas yield was lower than that reported in similar studies [21–24], while the yield of coke was higher, but in accordance with that reported else‐ where [21–24, 30].

3.3. Fractional distillation of OLP

3.3.1. Laboratory unit

Table 3 illustrates the material balances and yields of distillation products (distillates, bottoms,and gas) produced by laboratory fractional distillation of OLP obtained at 450°C and 1.0 atm,with 5, 10, and 15% (wt) Na2CO3 in pilot scale, using Vigreux columns of different heights (L1 =10 cm, L2 = 30 cm, L3 = 50 cm), operating without reflux. For the experiments carried out usingcolumns of different heights, with and without reflux, the yields of distillates (biofuels) andgas decreased in a smooth exponential and linear fashion, respectively, along with the columnheight, while that of bottoms products increased exponentially with increasing column height,as shown in Figure 2. The same tendency was observed by Dandik and Aksoy [6, 7]. The yieldof distillates of 66.26% (wt), obtained with a column of 10 cm, was equal to that reported byAlmeida et al. [23, 24], higher than that reported elsewhere [6, 7, 61, 64], and lower than thatreported by Kumar and Konwer [63]. In addition, the yields of gasoline, kerosene, light diesel,and heavy diesel of 1.55, 11.17, 21.38, and 32.72% (wt), obtained with a column of 10 cm, were inaccordance with the yields of distillation fractions reported by Almeida et al. [23, 24] and Kumarand Konwer [63]. For the experiments carried out with OLP obtained with 5, 10, and 15% (wt)Na2CO3, using a column of 50 cm height, with and without reflux, the yields of distillates (bio‐fuels) and gas increased in a sigmoid and linear fashion, respectively, with increasing catalystcontent, while those of bottoms products decreased in a sigmoid fashion, as shown in Figure 3.Dandik and Aksoy [7] observed the same tendency. The yield of distillates obtained with 15%(wt) Na2CO3 and 50 cm column height (62.15%) was higher than that reported by Dandik and160 Distillation - Innovative Applications and Modeling

Figure 3. Yield of distillation products (distillates, bottoms, and gas), produced by laboratory distillation with (YB,R, YR,R, and YG,R) and without reflux (YB, YR, and YG) with OLP obtained at 450°C and 1.0 atm, with 5, 10, and 15% (wt) Na2CO3 in pilot scale, using a column of 50 cm.

Aksoy [7] at 420°C, 1.0 atm, with 10% (wt) Na2CO3, using a fractionating column of 54 cm, but lower than the one obtained by Kumar and Konwer [63] using an Oldershaw column of 50 cm.

Table 4 shows the material balances and yields of distillation products (distillates, bottoms, and gas) produced by laboratory fractional distillation of OLP obtained at 450°C and 1.0 atm, with 5, 10, and 15% (wt) Na2CO3 in pilot scale, using Vigreux columns of different heights (L1 = 10 cm, L2 = 30 cm, L3 = 50 cm), operating with reflux. The results show higher distillate yields and lower bottoms products yields compared to the fractional distillation without reflux, as well as the absence of heavy diesel‐like fractions. In addition, the same tendency was observed for the variation of distillates, bottoms products, and gas yields with increasing column heights by fractional distillation of OLP obtained with 15% (wt) Na2CO3 and with a 50 cm column by fractional distillation of OLP obtained with 5, 10, and 15% (wt) Na2CO3. For the experiments with different column heights, a maximum distillate yield of 89.44% (wt) was achieved at 10 cm, much higher than those reported elsewhere [6, 7, 23, 24, 61, 63, 64], showing that reflux has improved the yields of distillates. This is according to the results of Kumar and Konwer [63] for the global yield of distillation fractions collected between 180 and 300°C, 300 and 325°C, and 325 and 370°C, operating with a reflux ratio of 0.2 and 10 mm Hg, obtaining 56.80% (wt). In addition, the yields of gasoline, kerosene, and light diesel of 10.86, 15.38, and 63.18% (wt) were according to the yields of gasoline (14.32%), kerosene (8.67%), and diesel (56.80%) reported by Kumar and Konwer [63]. For the experiments using a column of 50 cm height and OLP obtained with 5, 10, and 15% (wt) Na2CO3, a maximum distillate yield of 71.65% (wt) was achieved for OLP obtained with 15% (wt) Na2CO3, much higher than those reported elsewhere [6, 7, 23, 24, 61, 64], but lower than those reported by Kumar and Konwer [63]. Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 163 http://dx.doi.org/10.5772/66759

Yield of biofuels 89.44 83.30 71.65 68.38 69.77 71.65

Yield of gas (wt%) 3.74 5.81 5.95 3.90 5.10 5.95

Yield of raffinate 6.18 10.00 22.24 27.72 25.13 22.24

TB,I, initial boiling temperature; TB, boiling temperature.

Table 4. Mass balances and yields of distillation products produced by laboratory fractional distillation of OLP obtained at 450°C and 1.0 atm, with 5, 10, and 15% (wt) Na2CO3 in pilot scale, using Vigreux columns of 10, 30, and 50 cm, operating with reflux.

3.3.2. Pilot unit

Material balances and yields of distillation products produced by pilot fractional distilla‐ tion of OLP, obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3 in pilot scale, using a differential distillation apparatus, packed with borosilicate‐glass raschig rings of cylindri‐ cal geometry (ID = 1.0 cm, L = 1.0 cm), of 100 cm height, with internal reflux, are illustrated in Table 5. The results show a distillates yield of 32.68% (wt), higher than that reported by Dandik and Aksoy [7] at 400 and 420°C, column height of 54 cm, with 1, 5, and 10% (wt) Na2CO3, but lower than the one obtained by Kumar and Konwer [63], collected between 40 and 140°C, 140 and 180°C, and 180 and 300°C, being the last fraction performed with a reflux ratio of 0.2 and 10 mm Hg. The yield of distillates in pilot distillation scale was lower because of the higher column height, and the fact that distillation was carried out up to 280°C because of equipment instabilities. The distillation of OLP, obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3, using a differential distillation apparatus, packed with borosilicate‐glass raschig rings, of 100 cm height, with internal reflux, improved the qual‐ ity (physicochemical properties) of gasoline, kerosene, and light diesel‐like hydrocarbon fractions, particularly the acid values. The acid values ranged between 0.334 and 0.420 mg KOH/g, below the maximum permitted (0.5 mg KOH/g) acid value limit specification for diesel fuel S10 of ANP 65 [67]. Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 165 http://dx.doi.org/10.5772/66759

Process parameters Column height (cm)

100Initial temperature (°C) 30

Final temperature (°C) 305

Processing time (min) 270

Distillation fractions TB,I (°C)

(40ºC < TB < 175ºC) 94.6

(175ºC < T < 235ºC)

B 174.9

(235ºC < T < 280ºC)

B 233.8

Distillation fractions (material balances)

Mass of feed (g) 6100.00

Mass distillation fraction (40°C < T < 175ºC) (g)

B 241.34

Mass distillation fraction (175°C < T < 235ºC) (g)

B 631.24

Mass distillation fraction (235°C < TB < 280ºC) (g) 1121.15

Mass bottoms products (raffinate) (g) 4106.27

Yield of gasoline‐like fraction (wt%) 3.95

Yield of kerosene‐like fraction (wt%) 10.35

Yield of light diesel‐like fraction (wt%) 18.38

Yield of heavy diesel‐like fraction (wt%) –

Yield of biofuels (wt%) 32.68

Yield of raffinate (wt%) 67.32

T , initial boiling temperature; T , boiling temperature.

B,I B

Table 5. Mass balances and yields of distillation products (distillates and bottoms) produced by pilot fractionaldistillation of OLP obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3 in pilot scale, using a differential distillation‐packed column of 100 cm, with internal reflux.

3.4. Physicochemical properties of distillation fractions

3.4.1. Density of distillation fractions

Physicochemical properties of hydrocarbon‐like fractions, produced by laboratory fractional dis‐

tillation of OLP, using Vigreux columns of different heights (L1 = 10 cm, L2 = 30 cm, L3 = 50 cm),operating with and without reflux, and a pilot differential distillation column, packed with boro‐silicate‐glass raschig rings, of 100 cm height, with internal reflux, are illustrated in Tables 6–8.The density of distillation fractions, produced by laboratory distillation of OLP at 450°C and1.0 atm, with 15% (wt) Na2CO3, with and without reflux using columns of different heights(L1 = 10 cm, L2 = 30 cm, L3 = 50 cm), and a pilot‐packed distillation column of 100 cm, with inter‐nal reflux, is shown in Figure 4. One may observe that densities of distillation fractions increasewith increasing boiling temperature intervals, as reported by Kumar and Konver [63], remaining 166

almost constant along with the column height for the experiments carried out in laboratory scale,with and without reflux. For the distillation experiments carried out in laboratory scale withoutreflux, a total of four hydrocarbon‐like fractions were collected (gasoline, kerosene, light diesel,and heavy diesel), while for the experiments under reflux conditions, only three hydrocarbon‐like fractions could be collected (gasoline, kerosene, and light diesel). This is probably because ofthe recycling of part of the distillates back into the distillation column. In addition, the densitiesof gasoline, kerosene, and light diesel produced by fractional distillation in laboratory scale withreflux superposed exactly those of kerosene, light diesel, and heavy diesel produced by fractionaldistillation in laboratory scale without reflux, showing the importance of operating under reflux170 Distillation - Innovative Applications and Modeling

Figure 4. Density of hydrocarbon‐like fractions produced by laboratory distillation of OLP obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3, with and without reflux using columns of 10, 30, and 50 cm, and a pilot‐packed distillation column of 100 cm.

conditions to separate properly the hydrocarbon‐like fractions. The densities of hydrocarbon‐like

fractions produced by fractional distillation in pilot scale, using a differential distillation column, packed with borosilicate‐glass raschig rings, of 100 cm height, were lower in comparison to those produced by fractional distillation in laboratory scale, with and without reflux. Finally, the use of reflux made it possible to cut the hydrocarbon‐like fractions properly, correcting the lower density limits, as observed by Almeida et al. [22–24], and thus matching the densities of kerosene and diesel fuels according to kerosene aviation specifications (QVA‐1/JET A‐1) of ANP 37 [68] and diesel S10 specification of ANP 65 [67].

3.4.2. Acid values of distillation fractions

The acid values of hydrocarbon‐like fractions, produced by laboratory distillation of OLP

(450°C and 1.0 atm, with 15% (wt) Na2CO3), without reflux using columns of different heights (L1 = 10 cm, L2 = 30 cm, L3 = 50 cm), and a pilot‐packed distillation column of 100 cm, with internal reflux, are illustrated in Figure 5. The acid values of hydrocarbon‐like fractions decreased in a linear fashion with increasing column height for the experiments carried out in laboratory scale, without reflux, as shown in Figure 5. This is probably caused by the con‐ centration of lighter volatile compounds in the vapor phase with increasing column height, so that the chemical compounds conferring the acidity of hydrocarbon‐like fractions, par‐ ticularly those of medium and long carbon chain length present in OLP, cannot reach the top of the d ­ istillation column, being present in small concentrations in the gaseous phase. The Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 171 http://dx.doi.org/10.5772/66759

Figure 5. Acid values of distillation fractions produced by laboratory distillation of OLP obtained at 450°C and 1.0 atm,with 15% (wt) Na2CO3, without reflux using columns of 10, 30, and 50 cm, and a pilot‐packed distillation column of 100 cmheight.

acid ­values of distillation fractions also decreased with increasing boiling temperature ranges,except the heavy diesel‐like fraction, which is in accordance with the results reported byElkasabi et al. [64], for acid values of tail‐gas reactive pyrolysis (TGRP) distillation fractions.The acid values of hydrocarbon‐like fractions decreased with increasing Na2CO3 content, fordistillation experiments in laboratory scale, using a column of 50 cm, with and without reflux,showing that fractional distillation of OLP with high acid values was ineffective. The acidvalues of hydrocarbon‐like fractions produced by fractional distillation in pilot scale, using adifferential distillation column, packed with borosilicate‐glass raschig rings, of 100 cm height,were lower in comparison to those produced by fractional distillation in laboratory scale, withand without reflux. This showed that use of packed distillation columns improved not onlythe de‐acidification process, but also the physicochemical properties of distillation fractions.

identification of absorption bands/peaks was done according to previous studies [21, 24]. The spectrum of OLP obtained with 5% (wt) Na2CO3 presented a wide band of axial deforma‐ tion at 3435 cm–1 compared to OLP obtained with 10 and 15% (wt) Na2CO3, characteristic of O–H intramolecular hydrogen bond, indicating probably the presence of fatty alcohols and/or carboxylic acids. This band was also observed for gasoline and kerosene‐like frac‐ tions, using a pilot‐packed distillation column of 100 cm height, as well as light diesel‐like fraction, using columns of 10, 30, and 50 cm height, without reflux, both obtained by distil‐ lation of OLP at 450°C and 1.0 atm, with 15% (wt) Na2CO3. The spectra of OLP and distil‐ lation fractions exhibited intense peaks between 2921 and 2964 cm–1 and between 2858 and 2964 cm–1, indicating the presence of aliphatic compounds associated with methylene (CH2) and methyl (CH3) groups. This confirmed the presence of hydrocarbons [21–24]. One can also observe for OLP and distillation fractions, except for light diesel‐like fraction, produced by ­laboratory ­distillation without reflux, using columns of 10 cm, the presence of bands at Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 173 http://dx.doi.org/10.5772/66759

Figure 7. FT‐IR of hydrocarbon‐like fractions produced in a pilot‐packed distillation column with internal reflux of 100cm height with OLP obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3 in pilot scale.

2361 cm–1, ­characteristic of asymmetrical axial deformation of CO2. In addition, both OLPobtained at 450°C and 1.0 atm, with 5% (wt) Na2CO3, exhibited the presence of an intense andlarger axial deformation band between 3200 and 2500 cm–1, characteristic of hydroxyl (O–H)groups [39, 40], indicating the absence of carboxylic acids. This is according to the OLP acidvalue of 51.56 mg KOH/g. An intense axial deformation band has been observed for OLP,whose intensity decreases with Na2CO3 content, characteristic of carbonyl (C=O) groups,with peaks at 1742, 1745, and 1747 cm–1 probably associated with a ketone and/or carboxylicacids [21–24]. This is according to the acid values of OLP presented in Table 1, with its high‐est value obtained with 5% (wt) Na2CO3. These peaks were also observed in kerosene, pro‐duced by pilot‐scale distillation, and light diesel, produced by laboratory distillation withoutreflux, using columns of 30 cm. The spectra of OLP and distillation fractions were exhibitedbetween 1455 and 1465 cm–1, a characteristic asymmetrical deformation vibration of methy‐lene (CH2) and methyl (CH3) groups, indicating the presence of alkanes [21–24]. The spectrumof OLP and distillation ­fractions was identified at 1377 cm–1, except for light diesel, produced174 Distillation - Innovative Applications and Modeling

Figure 8. FT‐IR of light diesel‐like hydrocarbon fraction produced by laboratory distillation without reflux using columns of 10, 30, and 50 cm height with OLP obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3 in pilot scale.

by pilot‐scale distillation and by laboratory distillation without reflux, using columns of 50

cm, a band of symmetrical angular deformation of C–H bonds in the methyl group (CH3) [21–24]. The peaks between 995 and 905 cm–1 for OLP and distillation fractions were charac‐ teristic of an angular deformation outside the plane of C–H bonds, indicating the presence of alkenes [21–24]. The spectra of OLP and light diesel fraction exhibited bands between 721 and 667 cm–1, peaks characteristic of an angular deformation outside the plane of C–H bonds in the methylene (CH2) group, indicating the presence of olefins [21–24]. The FT‐IR analysis of OLP identified the presence of aliphatic groups (alkenes, alkanes, etc.), as well as oxygen‐ ates (carboxylic acids, ketones, fatty alcohols), and the presence of aliphatic groups (alkenes, alkanes, etc.) in light diesel fraction. Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 175 http://dx.doi.org/10.5772/66759

3.5.2. GC‐MS of OLP and light diesel‐like hydrocarbon fraction

Figures 9 and 10 illustrate the chromatograms of OLP obtained by catalytic cracking of palmoil at 450°C and 1.0 atm, with 15% (wt) Na2CO3 in pilot scale and light diesel‐like hydro‐carbon fraction produced by fractional distillation, using a pilot‐packed distillation columnwith internal reflux of 100 cm height. The classes of compounds, summation of peak areas,and retention times of chemical compounds identified by GC‐MS of OLP obtained at 450°Cand 1.0 atm, with 15% (wt) Na2CO3 and light diesel‐like fraction produced by pilot fractionaldistillation of OLP, using a differential distillation column of 100 cm height, are describedin Table 9. GC‐MS detected the presence of hydrocarbons such as alkenes, alkanes, alkynes,ring‐containing alkenes, ring‐containing alkanes, and dienes, as well as oxygenates such asketones and fatty alcohols. OLP is composed of 92.84% (area) hydrocarbons (52.72% alkenes,27.53% alkanes, 4.20% ring‐containing alkenes, 6.33% ring‐containing alkanes, and 1.21%dienes) and 7.16% (area) oxygenates (4.50% ketones and 2.66% fatty alcohols), while the lightdiesel‐like fraction is composed of 100% hydrocarbons (57.08% alkenes, 34.85% alkanes, and8.07% ring‐containing alkanes). In both OLP and light diesel‐like fraction, GC‐MS had notidentified the presence of carboxylic acids. The results were in accordance with the low acidvalues of OLP (3.55 mg KOH/g) and light diesel‐like fraction (0.34 mg KOH/g) presented inTables 1 and 8. The concentration of hydrocarbons in OLP, expressed in % (area), was highercompared to similar studies reported in the literature [21–24]. The chemical composition ofOLP indicated the presence of heavy gasoline compounds with C9 and C10 (C5–C10), kerosene‐like fractions (C11–C12), light diesel‐like fractions (C13–C17), and light heavy diesel compoundswith C18 and C19 (C18–C25), as reported in the literature [22–24]. The light diesel‐like fractionpresented carbon chain lengths between C10 and C20 with the following carbon chain lengths:alkenes C10–C20, alkanes C10–C16, and ring‐containing alkanes C11–C12. It may be observed that

OLP, 15% (wt) Light diesel‐like fraction, 15% (wt)

Class of compounds: RT (min) Class of compounds: RT (min)

chemical compounds chemical compounds Alkynes

6‐Tridecyne 6.96

Ʃ (Area%) = 0.85

Ketones

2‐Pentadecanone 14.14

2‐Nonadecanone 17.42

Ʃ (Area%) = 4.50

Alcohols

Oleyl alcohol 11.43

Ʃ (Area%) = 2.66

Table 9. Classes of compounds, summation of peak areas, and retention times of chemical compounds identified by CG‐MS of OLP obtained at 450°C and 1.0 atm, with 15% (wt) Na2CO3 and light diesel‐like fraction produced by pilot fractional distillation of OLP, using a differential distillation column of 100 cm height.

the presence of gasoline heavy compounds with C10 (C5–C10), kerosene fractions (C11–C12), and light heavy diesel compounds with C18, C19, and C20 (C18–C25) in light diesel‐like frac‐ tion, showed that fractional distillation in a pilot‐packed distillation column of 100 cm with internal reflux was not capable of proper separation of the hydrocarbon‐like fractions. This is probably caused by the limitation of internal reflux.

4. Conclusions

The yields of distillates and gas decreased along with the column height, while that of bot‐ toms products increased, for experiments with and without reflux. The yields of distillates and gas increased with increasing catalyst content, while that of bottoms products decreased. In addition, distillation under reflux conditions showed higher distillates yields and lower bottoms products yields compared to the fractional distillation without reflux, as well as the absence of heavy diesel‐like fractions. The densities of distillation fractions increased with increasing boiling temperature intervals, remaining almost constant along with the column height. In addition, the densities of gasoline, kerosene, and light diesel produced by fractional distillation in laboratory scale with reflux superposed exactly those of kerosene, light diesel, and heavy diesel produced by fractional distillation in laboratory scale without reflux, show‐ ing the importance of operating under reflux. The use of reflux made it possible to cut the hydrocarbon‐like fractions properly, correcting the lower density limits. The acid values of hydrocarbon‐like fractions decreased with increasing column height for the experiments with and without reflux. The acid values of distillation fractions showed a tendency to decrease Fractional Distillation of Organic Liquid Compounds Produced by Catalytic Cracking of Fats, Oils, and Grease 179 http://dx.doi.org/10.5772/66759

with increasing boiling temperature ranges. In addition, acid values of distillation fractionsdecreased with increasing Na2CO3 content, for distillation experiments using a column of50 cm, with and without reflux. The distillation experiments in pilot scale showed gasoline,kerosene, and light diesel‐like acid values of 0.33, 0.42, and 0.34 mg KOH/g, proving that useof packed distillation columns improved not only the de‐acidification process, but also thephysicochemical properties of distillation fractions. FT‐IR of OLP and distillation fractionsidentified the presence of aliphatic hydrocarbons (alkanes, alkenes, etc.) and the absence ofcarbonyl groups. The light diesel‐like fraction was composed of 100% hydrocarbons with anacid value of 0.34 mg KOH/g, density of 0.7862 g/cm3, and kinematic viscosity of 1.52 mm2 s–1,proving the technical feasibility of OLP de‐acidification by the fractional distillation process.

[67] ANP No. 65, 9.12.2011—DOU 12.12.2011

[68] ANP No. 37, 01.12.2009—DOU 02.12.2009

Energy Evaluation of the Use of an Absorption Heat

Pump in Water Distillation Process

Rosenberg J. Romero and Sotsil Silva-Sotelo

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67094

Abstract

It is impossible to transform the whole energy into useful work. It is impossible to increase the processes of cultivation of foods without water. It is impossible to separate all ions and minerals from water. Most of the real processes are thermodynamically irreversible. Calculations may indicate the fraction of efficiency of a thermal process. All the above mentioned facts have led to some proposals of cycles that exchange energy in order to produce a useful effect for the society. The key sustainable related parts are: to obtain water free of minerals or ions by distillation process. In this chapter, thermodynamic cycles will be explained for distillation using thermodynamic cycles of thermal machines called absorption heat pumps (AHPs). Distillation process offers to the AHPs an oppor- tunity to diminish the consumptions of fossil fuels. The AHPs are able to work with 2% of mechanical energy to carry out a sustainable distillation process. Most of the energy of an absorption heat pump operation is thermal energy. The operation of the AHPs are defined with the coefficient of performance (COP); the variations of this parameter are shown as function of the different scenarios to obtain sustainable distilled water.

Keywords: distillation, absorption heat pump, thermodynamic cycles

1. Introduction

One of the most useful processes for the sustainability would consider the efficient use ofenergy, water, and foods. Regrettably to include these three participants involves a pro-cess of consumption of those. It is impossible to transform the whole energy into usefulwork. It is impossible to increase the processes of cultivation of foods without water. It isimpossible to separate all ions and minerals from water. The thermodynamics has identi-fied the processes like reversible or irreversible process. Most of the real processes are186 Distillation - Innovative Applications and Modeling

irreversible. Calculations may indicate the fraction of efficiency of a thermal process. All the abovementioned facts have led to some proposals of cycles that exchange energy and matter with its surroundings, in order to produce a useful effect for the society. Excepting the production of foods, both key sustainable parts are related: to obtain water free of min- erals or ions, it can be carried out with distillation process. In this chapter, thermodynamic cycles will be explained for distillation using thermodynamic cycles of thermal machines called absorption heat pumps (AHPs). The main advantage of an absorption heat pump is that almost the whole energy that manipulates is thermal. Opposing to the conventional water purification systems, smaller energy is required to carry out the purification. The biggest difference with the heat exchanger is that it carries out the purification of water at different thermal levels. In the case of a heat exchanger, the energy source, where the energy comes, is at a higher thermal level (see Figure 1).

Figure 1. Thermal levels for water distillation.

2. Absorption heat pump

An absorption heat pump is a physic-chemical device made for use of sustainable thermal energy.

One of the obstacles of the technology is the ignorance that one has of them. The heat pumps are a type of thermal machines with subtle popularization. The basic concept is an analogy Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 187 http://dx.doi.org/10.5772/67094

with a mechanical pump for water. A mechanical pump for water drains water from a lowerlevel, and by application of mechanical energy, the water goes to a higher level. In similarway, a heat pump takes energy at a lower level and sends it to a higher level, using a part ofmechanical energy. This process actually happens, and it is called compression heat pumps(CHPs). If same process happens with thermal energy, then it is called absorption heat pump.The energy may go into a heat pump from several kinds of sources:

• Geothermal [1–7],

• Solar [8–11],

• Natural gas [12–14],

• Air [15–19],

• Groundwater [20–22]

• Even from mechanical energy [23, 24]

• Coal process [25–27]

The next section details the characteristics for compression and absorption heat pumps.

2.1. Compression heat pumps

A mechanical vapor compression heat pump (CHP) is a mechanical device that works withmechanical energy. The process that happens into a CHP is a thermodynamic cycle withtwo operations: compression and expansion (see Figure 2). CHP needs a fluid with the abil-ity to change from liquid to gas. The operating conditions are constants for pressure andtemperature all the time. Required energy for these changes is mechanical energy. Energycomes from lower temperature energy to the evaporator at the lowest pressure in the cycle.The delivering energy from CHP to the surroundings (i.e., for water distillation) goes at thehighest pressure in the condenser. This process is a cycle, and it requires intermittent orconstant energy [28].

2.2. Absorption heat pump

An absorption heat pump (AHP) is a mechanical device that does same function as CHP. Itsubstitutes the compressor by two additional thermal components. The permanent compo-nents for a heat pump are a condenser and an evaporator. The additional thermal componentswhich turn a CHP into an AHP are a vapor generator or called desorber and vapor absorber.

The AHP is classified in a simple way [29]: Type I if condenser temperature is higher thanevaporator temperature (TCO > TEV) and Type II if condenser temperature is lower than evapo-rator temperature (TCO < TEV).

Type I AHP is called “conventional heat pumps,” and Type II AHP is called “inverse heatpumps” or “absorption heat transformers.”188 Distillation - Innovative Applications and Modeling

Figure 2. Schematic diagram for compression heat pump.

2.2.1. Type I heat pumps

For heat pumping, an AHP really does a useful energy transference from a lower tempera- ture-level source of energy, free of cost (i.e., air, water, or soil) to a higher temperature level. The cycle is divided into two parts: the first part is a “working fluid” desorption from liquid absorbent at the highest temperature in the system. The second part happens at lower temper- ature and lower pressure for easy energy transference. When “working fluid” goes in vapor phase with liquid absorbent (separated in the first part), then a heat delivering at intermedi- ate temperature occurs. When vapor is condensed at the highest pressure, it delivers heat at intermediate temperature also. These processes may be possible to obtain almost two thermal Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 189 http://dx.doi.org/10.5772/67094

energy units for each thermal energy unit with cost, because the energy with no cost from air,water, or soil is able permanently.

Figure 3 shows schematically these processes. There are three thermal levels in a Type I AHP.Figure 4 shows the pressure zones and the thermal levels for the particular processes into thethermodynamic cycle.

The high pressure zone is useful for thermodynamic explanation. For a “pair” (“work-ing fluid” and “absorbent”) like water-lithium bromide, the vapor generation happens at

Figure 3. Absorption heat pump (Type 1) schematic concept.

190 Distillation - Innovative Applications and Modeling

t­ emperatures lower than 100°C because there is vacuum pressure, and then the concept of relative pressure is essential.

Figure 4. Absorption heat pump schematic cycle.

The thermodynamic cycle starts with energy going to “vapor generator” at higher tempera- ture and higher relative pressure. The “working fluid” is separated from “absorbent,” and it condensates in condenser unit. The condensation process releases useful energy but at lower energy level than “vapor generator.” The liquid from condenser is expanded to the evaporator. In evaporator, “working fluid” is placed in contact with a free cost of energy source (air, water, or soil) at the lowest temperature level of the cycle. This temperature defines the pressure value of the entire lower pressure zone. The evaporator generates vaporized working fluid a low tem- perature by low-pressure condition while the absorbent with diminished working fluid mass concentration is expanded from the “generator” to the absorber. The liquid that is coming from the generator is placed with the vaporized working fluid into the absorber, and this process delivers useful energy at intermediate temperature. The result for this cycle is that there are two components delivering useful heat for just one energy entry. The solution with absorbent and working fluid is pumping to the generator to restart the cycle. The energy balance is obvious:

​ ​Q​ GE​ + ​Q​ EV​ = ​Q​ CO​ + ​Q​ AB​​ (1) where QGE is the heat at the highest relative temperature entering to the “vapor generator” in the AHP, QEV is the heat at the lowest temperature level and coming from free cost of energy source, QCO is the useful energy at intermediate temperature caused by latent heat from vaporized “working fluid” originated in the generator, and QAB is the useful heat deliv- ering for the junction of absorbent with working fluid at lower relative pressure. Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 191 http://dx.doi.org/10.5772/67094

The thermal efficiency for thermal machines is based on “coefficient of performance” (COP).This COP is defined for each system. For this AHP, the COP is defined as the ratio of usefulenergy by energy with cost. In this AHP process, the pumping work is negligible because thatis around 1% of the thermal energy: ​Q​ ​ + ​Q​ ​ ​COP​ I​ = ​_______ ​ CO​Q​ ​ AB ​​ (2) GE

This dimensionless value allows comparison with other technologies even with differentpower capacities, higher or lower. A COP value equal to 1 means all entering energy in theAHP is useful. Values higher than 1 mean that cost-free energy is added to useful energy.

2.2.2. Type II absorption heat pumps

The main difference between Type I and Type II absorption heat pumps (AHP) is basicallythe switch between the pressure zones. Figure 5 shows the pressure and temperature levels tonote that difference in the operation modes.

Figure 5. Type I and Type II absorption heat pumps.

192 Distillation - Innovative Applications and Modeling

Unit operations for both AHP types are the same, but they happen at different pressure and temperature values. So, the mass balance is same for Type I and Type II AHP.

The cycle occurs in similar way (see Figure 6). Thermal energy enters to generator and evapo- rator. Thermal energy is delivered in absorber and condenser. The main advantage is that energy is added at intermediate temperature level, and useful energy is delivered at higher energy level but only in absorber component.

Figure 6. Absorption heat pump (Type 2) schematic concept.

This process has a particular implication: this is the unique technology that transforms ther- mal energy to mechanical pressure lift to deliver energy at higher temperature than the energy source.

Cycle starts when energy enters to the generator and evaporator. The generator splits work- ing fluid in vapor phase from absorbent. The working fluid is pumping through the evapora- tor. Evaporator is at higher relative pressure. Evaporator changes to vapor phase from the working fluid. This vapor is contacting with liquid absorbent into the absorber. The liquid absorbent comes from the generator at intermediate temperature. The absorption process delivers energy at the highest pressure in the system. The diluted solution returns to the gen- erator to restart the cycle. Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 193 http://dx.doi.org/10.5772/67094

COP for Type II AHP, with negligible 2 % of pumping work, is

​Q​ ​ ​COP​ II​ = ​_______ ​ ​Q​ ​ + ​ AB ​​ Q​ ​ (3) GE EV

This dimensionless value is lower than the unit because the utilized energy is used as part forpressure lift and other energy parts are revalorized. It is notorious to think that if energy comesfrom renewable energy or waste heat [30], then the results of the CO2 emission diminish.

3. Distillation process

Distillation process is expensive energetically. This process has two parts: the first part is torise the liquid’s temperature from an actual condition to saturation point, and the second partis to add a lot of energy to phase change process. This process has two processes, and everypart has inefficiency depending on heat transfer process into vapor phase or gaseous phase.

3.1. Water distillation

Water distillation with heat pump is no new [31–33]. However, it has lower reports [34]. Thecitation to papers indicates that some systems have been implemented for that purpose. Theinstallation has two main problems: low efficiency for comparison with other technologies[35–39] and higher cost compared with conventional systems [40].Type II AHPs are called “absorption heat transformers” also, and those have been reportedfor water distillation evaluation [41, 42]. Some configuration has success like “solar ponds”coupled to “absorption heat transformer” [43–45] and solar systems [46] among others renew-able energies [33].The main objective for this technology is to obtain mineral-free water with lower ambientimpact [47, 48].

4. Water distillation with absorption heat pumps

Water distillation from seawater or wells may be realized with AHP with a great advantage:lower ambient emission [32, 49, 50] in order to optimize the water distillation with the mini-mal energy supply [51].The modeling for this process has been previously reported with author’s collaborators (i.e.,[52]) that is based on mass and energy balances. It has assumptions and considerations foriterative calculation at steady-state conditions. The assumptions are close to reality to identify194 Distillation - Innovative Applications and Modeling

potential operating conditions for water distillation with Type I and Type II AHPs, with a huge amount of waste heat or renewable lower temperature heat.

4.1. Operating conditions

Water distillation requires a constant higher thermal energy. This temperature is a function of sea-level altitude at atmospheric pressure. It is not recommendable to include a vacuum process or artificial pressure increase for water distillation because those increase the energy consumption for mineral separation from distilled water [53]. For this reason, this chapter shows pairs based on water-lithium bromide for water distillation purposes for both AHP modes: Type I and Type II with: • Lithium bromide-water • Lithium bromide-ethylene glycol-water (called Carrol [29]) There is a possibility to use advanced AHP (double absorption or double stage [33]), but those configurations have lower COP values, and then they are not shown in the next results. Operating conditions are calculated for water distillation at a sea-level atmospheric pressure.

5. Results

The results are based on dimensionless COP that means how many energy is used for water distillation as function of each thermal energy unit added to the AHP. Of course, this dimen- sionless COP allows the comparison between the AHP systems. Figure 7 shows the ratio of energy used for distillation of water with a Type I AHP using water-lithium bromide. It is clear that all energy is not useful. Some part is a waste into the cycle, while evaporator temperature is closed to ambient temperature. The best operating conditions for this distillation are for waste heat at 160°C, with a preheating treatment for water saturation at 80°C and distillation into the absorber component at 105°C. Figure 8 shows the dimensionless COP for comparison with water-lithium bromide-ethylene glycol as additive to avoid risk in crystallization for lithium bromide. The additive has no variation in the used energy for water distillation. The dimensionless value is almost same for water distillation process at same operating conditions, but there is a variation of 10% away from risk into actual operation for leak of fracture in tubes. Figure 9 shows the proposal of Type II AHP for water distillation using water-lithium bromide. This is a great opportunity to operate a cycle with revalorization of waste energy. The dimensionless COP value is lower than of Type I, as expected. But the temperature values are lower. Water distillation happens with only 80°C heat source, at 20°C in the ambient temperature. The thermal efficiency goes from 0.38 to 0.48 for waste heat. This is a notorious result. It is not necessary to raise energy at 100°C to water distillation. This tech- nology allows distillation for well water with renewable energy lower than conventional machines. Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 195 http://dx.doi.org/10.5772/67094

Figure 7. Dimensionless COP Type I AHP for water distillation.

Figure 8. Dimensionless COP Type I AHP for water distillation.

Finally, Figure 10 shows a variation of the last operation conditions. The additive ethylene glycol is used to avoid crystallization. There is no variation in thermodynamic conditions for this distillation purpose, but safety for risk in crystallization is obvious. This actual operation avoids risk around 90% compared to lithium bromide.

The distillation is possible with AHP with thermal efficiencies from 0.38 to 0.78 with no fossil fuels using water-lithium bromide-ethylene glycol as pair.

Figure 10. Dimensionless COP Type II AHP for water distillation operating with water – Carrol. Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 197 http://dx.doi.org/10.5772/67094

6. Conclusion

The energy-efficient policies with renewable energy integration are not an actual trend; thisis a requirement for sustainability. Renewable energies coupled to thermodynamic cycles forwater distillation have been reported previously for another authors with energy input ofPV + RO around 3–20 kWh/m3 and PV + WIND + RO around 3–16 kWh/m3.

For absorption heat pumps, the efficient energy use is obvious: the thermal energy for thesecycles (Type I and Type II) comes from waste energy or renewable energy; then there are noCO2 emissions, while these are operated and provide distilled water.

The cycles in this chapter show water distillation at atmospheric pressure with heat exchangeat 100°C with two stages: one in condenser unit to preheat the water and a second unit, theabsorber, for flash process. This combination allows a distilled energy at 3.75 kWh/m3 forType I absorption heat pump and 8.5 kWh/m3 for Type II absorption heat pump. These val-ues include the actual COP with a higher distilled water production at the higher evaporatortemperature in both types.

[44] Salata, F., & Coppi, M. (2014). A first approach study on the desalination of sea water using heat transformers powered by solar ponds, Applied Energy, 136, 611-618. Energy Evaluation of the Use of an Absorption Heat Pump in Water Distillation Process 201 http://dx.doi.org/10.5772/67094

Solar Membrane Distillation: Use of a Helically Coiled

Fiber

Adel Zrelli

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67653

Abstract Membrane distillation (MD) is a novel process introduced to overcome the disadvan- tages of the conventional distillation process. MD has gained much interest, principally, for its lower energy demand and higher rejection factors. Many configurations of the membrane module have been tested to improve the MD process. In this case, and in order to see the possibility of using the helically coiled fiber for MD coupled with solar energy, a mathematical model has been developed. This model describes the evolutions of permeate flow rate with the variation of inlet feed characteristics, solar flux, and so on. A comparison between the use of linear and helically-coiled fiber shows an enhance- ment of the temperature polarization coefficient about 6% for the case of the helical fiber and to have an improvement factor by 28%. For the case of the effect of solar energy on the permeate flow rate, an increase of 264% is remarked for the variation of the direct solar flux from 200 to 800 W/m2. However, a reduction of 12% for the permeate flux is obtained, when the inlet feed concentration grows from 10 to 300 g/l.

Water is abundant on Earth. The majority (97.2%) consists of seawater [1]. The rest iscomposed of 2.2% ice caps and glaciers (unusable directly), while fresh water, which is foundin lakes, rivers, and groundwater, is only 0.6% [2]. In addition, the distribution of this wateris very uneven. In fact, only 10 countries share 60% of freshwater reserves while 29 countriesare facing a shortage of fresh water. These countries are located in Africa and the Middle East[3]. However, these freshwater may not be potable. Allowing this globally, many countriesare below the threshold shortage of drinking water. The drinking water is a major issue for204 Distillation - Innovative Applications and Modeling

development and survival for humans [4]. This shortage is a result of poor management of reserves, water pollution, and population growth. Also, this water shortage affects nearly 80% of world’s population [5]. To overcome this shortage of drinking water, several solu- tions were presented among which are the desalination of brackish water or seawater. Mainly, the desalination technologies, used around the world, are the thermal with 33% of total capacity and membrane processes with 56% of total capacity [6]. The first type, thermal processes, is based on physical change in the water state. For this type, the two techniques, which gained great global interest to offer to yet effective solutions to desalinate water, are multistage flash distillation (MSF) and multi-effect distillation (MED) [7]. For the second type, which is the membrane processes, a membrane is used to separate the water from the saline water (brackish or seawater). In this case, the characteristics of the mem- brane (such as porosity, wettability, selectivity, electric charge, etc.) are so important in order to obtain a high efficiency for the membrane processes. The two main techniques, used in this type, are the reverse osmosis (RO) and the electrodialysis (ED) [6]. Each technique uses the ability of membranes to separate selectively salts and water from the saline water. These two types of desalination technologies (thermal and membrane processes) have a high- energy demand, and the process performance is limited by the osmotic pressure or concen- tration polarization. In order to overcome these drawbacks, a promising alternative technol- ogy for desalination is introduced, which is the membrane distillation (MD) due principally to lower energy cost and membrane fouling [8]. MD is composed of four configurations. These configurations are the direct contact membrane distillation (DCMD), the air gap membrane distillation (AGMD), the sweeping gas membrane distillation (SGMD), and the vacuum membrane distillation (VMD) [9]. VMD has attracted increasing interest for various applications. From energy consumption point of view, it could clearly compete with reverse osmosis, when coupled with alternate source of energy such as solar energy [10]. In order to couple VMD to solar energy, different configurations can be used. In this case, membrane can be placed in or out of the absorber of the solar collector. Furthermore, many configura- tions of the hollow fiber membrane can be used. Among these configurations, we found the linear and the helical fibers. In this chapter, a brief outline of the main thermal and membrane desalination processes will be presented. This will be followed by the exposure of the membrane distillation and its different configurations and the used hollow fiber geometries in order to increase the process performance. Therefore, this chapter attempts to develop a novel hollow fiber module design, which is the helically coiled fiber. A comparison of the performance of the helically coiled hollow fiber to those of linear fiber will be done. The effects of this novel configuration on the permeate flow rate and the temperature polarization coefficient will be highlighted. In addi- tion, the effects of the process conditions, such as the initial feed concentration and the solar radiation, on the permeate flow rate will be evaluated.

2. Desalination processes

The most important desalination processes are the thermal processes and membrane processes. Solar Membrane Distillation: Use of a Helically Coiled Fiber 205 http://dx.doi.org/10.5772/67653

2.1. Thermal processes

2.1.1. Multi-effect distillation (MED)

These processes are composed principally of multistage flash (MSF) and multi-effect distillation(MED). MED is the oldest technique applied for seawater desalination [11]. The MED principle isbased on heat transfer from the condensing steam to feed seawater or brine in a series of effects(Figure 1). In this case, the steam produced in the first effect was condensed to produce freshwater in the second effect. This latter effect was operated at slightly lower pressure and temper-ature than in the previous effect. The heat of steam condensation allows to evaporate a portion ofthe seawater contained in the second effect and so on. Thus, only the energy required for theevaporation in the first effect is of external origin. MED can work with a low steam temperatureas heat source (70–80 C) and the multiplication of effects allows to reduce the specific consump-tion. Therefore, the number of effects is usually between 8 and 16 [12, 13].

2.1.2. Multistage flash (MSF)

The MSF process comes in practice since the late 1950s [15]. The distillation was done, in this case,in a series of flash chambers. The generation of steam, from brackish water or seawater, was theresult of a pressure drop and not of heat exchange with condensing steam, which is the case ofMED. The principle is so simple, the brackish water or seawater was pressurized and heated tothe plant’s maximum allowable temperature (limited to about 110 C). Afterwards, this heatedliquid was introduced into a chamber maintained at slightly below the saturation vapor pressureof the water (Figure 2). This chamber pressure level induces the flash of a fraction of its watercontent into steam. This latter is converted into fresh water by condensation on heat exchangerwith a series of closed pipes, while the rest of the heated liquid continues flowing through a seriesof chambers. The number of chambers, for this technology, is between 20 and 25 [11, 14, 16].

2.2.1. ElectrodialysisElectrodialysis process (ED) is an electrochemical separation process, which has been in com-mercial use for desalination of brackish water since 1970s, particularly for small- and medium-scale processes. This process uses the electric direct current to remove the salt ions in thebrackish water. The latter passes between pairs of anion-exchange and cation-exchange mem-branes. The cations (positive ions) migrate from the brackish water toward the negativeelectrode through the cation-exchange membranes, which allow only cations to pass (Figure 3).On the other hand, the anions (negative ions) migrate toward the anode through the anion-exchange membranes. In a conventional process, a large number of alternating cation-exchange and anion-exchange membranes are stacked together, separated by flow spacers,which are plastic sheets that allow the passage of water. The total power consumption of EDunits ranges from 0.7 to 2.5 kWh/m3 of desalinated water for feed water salinity of 2500 ppmand from 2.64 to 5.5 kWh/m3 of desalinated water for feed water salinity of 5000 ppm [18–20].

2.2.2. Reverse osmosis

Reverse osmosis (RO) is a pressure-driven process that separates two solutions with differentconcentrations across a semi-permeable membrane (Figure 4). The rate of fresh water thatpenetrates the membrane depends on the difference between the applied pressure and theosmotic pressure of the feed salt water. The osmotic pressure is directly related to the saltconcentration in the saline water. For brackish water desalination, the operating pressuresrange from 18 to 28 bar, and for seawater desalination from 55 to 69 bar [21]. The discharge

Figure 4. Schematic diagram of RO desalination process.

208 Distillation - Innovative Applications and Modeling

brine from an RO unit ranges from 20 to 70% of the flow feed water, depending on salinity of the feed water, applied pressure, and type of membrane. Until today, the predominant desalination processes in use are RO and MSF, which constitute 53 and 25% of worldwide capacity, respectively (Figure 5). However, these processes have some disadvantages, which are described in the subsequent text.

They are considered energy intensive either by the heat demand for the MSF process (generally for the thermal processes) or by the high-pressure demand as in reverse osmosis. The used pressure for the RO process is about 10–15 bar for brackish water and 50–80 bar for seawater, and the consumed electrical energy, to produce 1 m3 of desalinated water, is in the range of 3–4 kWh [23]. This high-energy consumption contributes to further environmental problems such as more pollutants and undesired emissions. Other disadvantages of these processes are the high maintenance cost of the mechanical equipment and the limited membrane lifespan [24]. Also, reverse osmosis efficiency is strongly affected by the osmotic pressure of the highly concentrate feed solutions, which imply the use of high pressure and the reduction of the salt rejection with the decay by 50% of permeate flux [25]. These drawbacks push down the efficiency of those processes, which require the search for alternative, environment friendly, and sustainable desalination.

2.3. Membrane distillation

2.3.1. Membrane distillation principle

Membrane distillation (MD) is an alternative to the traditional evaporative distillation systems used for desalination or water purification processes. MD is a thermally driven membrane process developed over the last 60 years [26]. In this process, a hydrophobic microporous membrane separates a hot and cold stream (Figure 6). This membrane serves, also, as a physical support for vapor transport but a barrier to liquid penetration, thus allowing the separation of volatile and non-volatile species. In the case of salty water, the water (volatile

Figure 6. Principle of membrane distillation.

specie) passes through the membrane as vapor without salt and condenses on the low-temperature side and distillate is formed [27, 28].Some of advantages of MD processes over conventional desalination processes such as MSFand RO are as follows:• Lower working temperature, which leads to coupled MD to low-grade and renewable energy source such as solar energy.

• Outstanding rejection performance, of non-volatile solute, which can reach as high as 100%.• Performance is not significantly affected by high osmotic pressure or concentration polari- zation because the solution vapor pressure changes only marginally with salt concentra- tion.• Reduced chemical interaction between membrane and process solution [8, 25, 27, 29, 30].

2.3.2. MD configurationsMD can be classified into four different configurations according to the nature of the cold sideof the membrane [31]: the first configuration is the direct contact membrane distillation(DCMD) in which the membrane is in direct contact with liquid phases on both sides. Thevolatile components of the feed evaporate at the interface feed/membrane diffuse through the210 Distillation - Innovative Applications and Modeling

membrane pores and condensate at the cold side in the distillate stream [26–29]. The second configuration is air gap membrane distillation (AGMD) in which an air gap is interposed between the membrane and the condensate surface. This stagnant air gap reduces heat losses due to conduction, thus increasing the thermal efficiency of this configuration [32]. The sweeping gas membrane distillation (SGMD) represents the third configuration. In this configuration, a cold inert gas is used in permeate side as carrier for the produced vapor. The condensation of this vapor takes place outside the membrane module [8]. The fourth and the last configuration is the vacuum membrane distillation (VMD), in which the vapor phase is vacuumed from the liquid through the membrane and condensed outside of the membrane module [30].

VMD presents many advantages when compared to the other MD configurations by pres- enting the highest flux and desalination rate, and the lowest fresh water conductivity (Figures 7 and 8). For VMD, the two main advantages are a very low conductive heat loss and a reduced mass transfer resistance [30, 33–35].

2.3.3. Coupling MD with solar energy

Generally, desalination consumes much energy. In order to minimize the energy usage and consequently the cost, the use of renewable energy (wind, geothermal, solar, etc.) is a feasible and potential solution. In addition, the lack of drinkable water often accompanies the abun- dance of solar radiation, which makes favorable the coupling of the desalination processes with the solar energy [36]. In the case of VMD, the permeate flux could be enhanced, when it is coupled with solar energy, and its value can be increased from the range of (5–15 l/h m2) to that (40–85 l/h m2). Following this coupling of VMD with solar energy, this MD process could clearly compete with RO [37].

Figure 7. Comparison of flux for three configurations at different feed concentration [33]. Solar Membrane Distillation: Use of a Helically Coiled Fiber 211 http://dx.doi.org/10.5772/67653

Figure 8. Comparison of conductivity for three configurations at different feed concentration [33].

2.3.4. Module geometry configurations

In MD process, the most studied geometry configurations are flat sheet and hollow fibermembrane modules. The hollow fiber membrane modules are preferable due to their largermembrane area per unit volume and highest packing density of all module types and modularversatility. The hollow fiber packing density is about 3000 m2/m3 [8]. However, a poor config-uration of hollow fiber modules will result in the reduction of the permeate production and theefficiency of the MD process. In order to overcome this problem, many studies have focused onstrategies to improve the MD performance through designing novel membrane modules[38–41] and enhancing the permeate flux. In this case, the introduction of baffles (Figure 9), in

Figure 9. Hollow fiber module with window baffles [38].

212 Distillation - Innovative Applications and Modeling

membrane module, provides a better flow distribution and could increase the shell-side heat- transfer coefficients leading to 20–28% flux enhancement. Furthermore, the use of hollow fiber configurations with wavy geometries (twisted and braided (Figure 10)) led to flux enhancements as high as 36%.

Yang et al. [39] reported that the greatest enhancement is achieved by the modules with spacer-knitted (Figure 11) for which the flux is increased more than 90% when compared with the randomly packed module. For the same configuration (spacer-knitted) and when the operating conditions were modified, the flux enhancement achieved was only 51.8% [41].

Figure 11. Spacer-knitted design of hollow fiber module [39].

On the other hand, the other fiber configuration is the helically coiled fiber. Few studies havebeen undertaken on the use of this configuration. Among these studies, we present theMallubhota et al. study [42]. In this work, a comparison, for nanofiltration, between linearand helical modules was done. The results show an enhancement of the permeation rateduring their use of the helical module. This enhancement is due to the reduction membranefouling and polarization concentration. In addition, when the helical-coiled fiber was usedby Nagase et al. [43], an enhancement in the mass transfer coefficient and consequently in thepermeate rate has been observed. The same finding has been proved by Liu et al. when theyused this helical configuration in membrane extraction.

3. Use of helically coiled fiber

3.1. Design description

In our case, the solar desalination installation (shown in Figure 12) is composed of parabolictrough concentrator. At the focal axis, the absorber is mounted, which is in the shape of acylindrical tube. This absorber contains the hollow fiber membrane. This membrane has theshape of a coil and the configuration of an absorber, and the membrane is similar to a helicallycoiled heat exchanger. In addition to that, solar rays are focused into the absorber, and anincrease of the feed temperature is consequently reported.In order to have a symmetrical conception, we study a system that contains two helicallycoiled fibers (Figure 13). Since the flow is symmetric about a vertical plane passing throughthe axis of the cylinder, only the half-plane needs to be considered (Figure 14).214 Distillation - Innovative Applications and Modeling

Figure 12. Solar-VMD installation.

Figure 13. Basic geometry of a helical fiber.

Figure 14. Domain of study [44].

3.2. Mathematical model

Based on Figures 13 and 14, we developed a mathematical model and the following assump-tions are used for the numerical calculations:1. The flow is fully developed before it enters the inlet of the absorber.2. Fluid is incompressible and Newtonian.

3. The motion is considered as axisymmetric, hence, only half of the absorber is considered.4. The gravity force is neglected.5. All angular gradient parameters are negligible; the model is described in the coordinates r and z.6. No slip condition is valid on the surface of the fiber.

7. All simulations are carried out assuming steady state.

Under these conditions, the appropriate governing equations are written [45]:Continuity equation:

The water vapor pressure (Pinter) at the liquid/vapor interface may be related with the temper-ature, by using Antoine's equation [51]:

3841 Pinter ðTÞ ¼ exp 23:238 ð18Þ T 45

where Pinter (T) is in Pa and T is in K.

Following an analogy between the helically coiled fiber and the coiled tube heat exchanger, weused the correlation presented by Salimpour [52, 53], in order to calculate the outside heattransfer coefficient Nu ¼ 19:64Re0:513 Pr0:129 γ0:938 ð19Þ

P γ¼ ð20Þ 2πRc

The helically coil length (Lc) is given by

218 Distillation - Innovative Applications and Modeling

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ LþP Lc ¼ p2 þ ðπDcÞ2 ð21Þ P

For each “i” element of the absorber, we can calculate the permeate flow rate “m_ pi ” according to the below equation:

m_ pi ¼ J vi πLci do ð22Þ

The temperature polarization coefficient, TPC, is defined to measure the effective temperature difference between Ta and Tam. For VMD configuration, TPC is defined as

T am TPC ¼ ð23Þ Ta

The solution procedure and the flow chart of the calculation were presented in Ref. [54].

3.3. Effect of the coil pitch

In Figure 16, it is noticed that the permeate flow rate increases with the increase of the coil pitch to reach their maximum toward the pitch value equaling 32.2 mm and decreases thereafter [44]. It should be noted that when the pitch decreases, the size of the wake also decreases and the empty space between the fibers available for bulk flow is deceased. This leads to a decrease of the feed velocity and the Reynolds number, which causes a decrease of the boundary layer heat transfer coefficient and the permeate flux. However, when the pitch decreases, the fiber exchange surface increases (Figure 17). These two variations of permeate flux and fiber exchange surface lead to obtain the optimum pitch, which is 32.2 mm.

Figure 16. Effect of coil pitch on the permeate flow rate.

3.4. Effect of the distance between fiber and absorber internal wallIn order to optimize the distance between fiber and absorber internal wall, we have used thevalue of 32.2 mm for the coil pitch. After simulation, the obtained results are shown inFigure 18. In this figure, the reliance of the permeate flux on the coil radius is clear. As seen,the permeate flux increases sharply to reach their maximum toward the value of 4.3 mm for thedistance between fiber and absorber internal wall (95.7 mm for the coil radius) and decreasesthereafter. It is important to say that this decrease is due to the decrease of velocity, which isinfluenced by the width of the channel between the outside face of fiber and the absorberinterior wall. When the value of this width decreases, the effect of channel blockage isremarked. In addition, the parabolic profile of the inlet velocity leads to obtain decreasedvalues of velocity near the absorber interior wall [44].

3.5. Comparison between linear and helical fiber

In order to compare the coil to the linear fibers, we conserve all fiber characteristics and wechange only the geometric configuration. In the case of the linear configuration, we are inter-ested by the domain shown in Figure 19. Due to symmetry, the modeled domain is reduced tothat presented in Figure 20.

Figure 21 illustrates the obtained data for the variations of the TPC for the two fiber configu-rations. These fibers are used in VMD coupled with solar energy in order to increase thetemperature of the feed, which flow in the shell-side.220 Distillation - Innovative Applications and Modeling

Figure 18. Evolution of permeate flow rate with coil radius.

Figure 19. Linear fibers in the solar concentrator absorber.

The inlet feed velocity, in this case, was 3.4 · 104 m/s corresponding to a Reynolds number of 68 and the inlet feed temperature was 20 C. According to this figure, two similar evolutions, of the TPC along the module length, were shown for the two fiber configurations. The value of the TPC drops quickly as the module length increases from 0.1 to 0.3 for linear fiber and to 0.2 for helical fiber, and then decreases slowly when the module length increases to 1. For the linear fiber, the TPC decreases first from 0.8688 to 0.8543 and reaches the value of 0.8448 when the module length is 1. Also, for the helical fiber, the decrease, in the first, of the TPC was between 0.9205 and 0.8791 to reach, at the end, the value of 0.8695. However, the TPC of the helical fiber is greater than that of the linear fiber. The improvement factor of the TPC of the helical fiber is in the range of 3–6% compared to the linear one. This improvement can be explained by the fact Solar Membrane Distillation: Use of a Helically Coiled Fiber 221 http://dx.doi.org/10.5772/67653

Figure 20. Domain of the study for linear fiber.

that for the flow on the shell-side of the helical fiber, a cross flow is developed, of the hot feed inthe outside surface of the helical fiber, which allows to enhance the outside heat transfer coeffi-cient. Due to this enhancement, the interface outside membrane temperature (Tinter), for thehelical fiber, is greater to that for the linear fiber and in the same operating conditions.

3.5.2. Effect of fiber configuration in permeate flow rate

The improvement of Tinter leads to an increase of the permeate flow rate for the helical whencompared to the linear fiber (Figure 22). According to this figure, the evolutions of the permeateflow rate along the module length increase from 2.7 · 102 to 3.58 · 102 kg/h for the helical222 Distillation - Innovative Applications and Modeling

fiber and from 2.12 · 102 to 2.73 · 102 kg/h for the linear fiber. In this case, the permeate flow rate for the helical fiber is 0.2685 and 0.21 kg/h for the linear fiber. The improvement factor in this case is about 28%. For the two configurations and along the module, the bulk tempera- ture increases due to the solar rays focused on the exterior absorber wall. This increase in temperature raised the driving force, which is the vapor pressure difference, and the permeate flow rate. The difference between permeate flow rate for the helical and the linear fibers is principally due to the nature of the flow in the fiber outside. In the case of the helical fiber, the cross flow has an important influence on temperature polarization and permeate flow rate. However, cross flow on the shell-side yields a high heat transfer coefficient than parallel flow in the case of linear fiber.

3.5.3. Effect of feed flow rate

The effect of feed flow rate was investigated at the range of 20–60 l/h (Re: 34–102), while the feed temperature was maintained at 20 C. Figure 23 illustrates the variation of the ratio bet- ween helical and linear permeate flow rates with the feed flow rate. It was found that this ratio increases strongly from 20 to 40 l/h and then increases slowly from 1.28 to 1.31 when the feed flow increases from 40 to 60 l/h. It is important to remark that for the solar membrane distillation processes, the amount of energy collected is almost unchangeable for a specific day. For this reason and for our installation, the incident solar radiation is about 800 W/m2, when the feed flow exceeds 40 l/h, the residence time of the feed in the module decreases and the difference of the bulk temperature between the inlet temperature and the outlet temperature becomes smaller. So optimization of the feed flow rate is an effective way to obtain a high permeate flow rate in VMD coupled with solar. Solar Membrane Distillation: Use of a Helically Coiled Fiber 223 http://dx.doi.org/10.5772/67653

Figure 23. Effects of feed flow rate on the ratio of the helical and linear permeate flow [54].

3.5.4. Effect of inlet feed temperature

To obtain information about the effect of inlet feed temperature on the permeate flow rate, inboth fiber configurations, feed temperature was varied in the range of 20–80 C (Figure 24) andthe feed flow rate was fixed at 40 l/h. Permeate flow rates for both configurations showed anexponential relationship with inlet feed temperature. Although for a given flow rate, feedtemperature has a small effect on the Reynolds number. There are only limited changes inviscosity and density. But the enhancement of the permeate flow rate with the inlet feed temper-ature can be explained by the increase in vapor pressure (Eq. (18)), or driving force (Pinter-Pv),with temperature. The helical fiber had a higher permeated flow rate than that of the linear fiberfor all temperatures across the entire temperature range. Since the polarization coefficient tem-perature of the helical fiber was greater than in the linear fiber, Tinter in this case becomes close tothe feed bulk temperature (Tb). This leads to the evolution of the permeate flow rate between0.746 · 104 and 5.139 · 104 kg/s when the inlet feed temperature increases from 20 to 80 C.

3.6. Effect of inlet feed concentration

For our solar vacuum membrane distillation installation, when the inlet feed concentration wasvaried, the feed temperature and solute concentration rise along the module membrane andinfluence consequently the permeate flux, Jv, through the membrane. Due to this mass transfer,a temperature and solute concentration gradients are generated in the membrane liquid bound-ary layer. So, the bulk concentration, Ca, is different from the value at the surface of the mem-brane, Cam.224 Distillation - Innovative Applications and Modeling

This concentration can be calculated using the film model and the mass balance across the feed boundary layer as

Jv Cam ¼ Ca exp ð24Þ k c ρa

where kc is the film mass transfer coefficient and ρa is the bulk solution density. Ca and Cam can be used to calculate the concentration polarization coefficient, CPC, which measure the increase of solute concentration on the membrane surface

Cam CPC ¼ ð25Þ Ca

Figure 25 shows the effect of the inlet concentration of the feed on the permeate flux. It can be seen that the inlet concentration has a relatively small effect: increasing this concentration from 10 to 300 g/l reduces the permeate flux by only 12%. This moderate effect of the inlet feed concentration on the permeate flux is an advantage for our conception and generally for membrane distillation when it is compared to reverse osmosis system. A drop about 50% is obtained, for this process, when the inlet concentration was varied between 35 and 350 g/l [25]. Solar Membrane Distillation: Use of a Helically Coiled Fiber 225 http://dx.doi.org/10.5772/67653

In order to explain the drop of the permeate flux with the increase of the inlet concentration,several phenomena can be advanced. Among these phenomena, we find the temperaturepolarization, the concentration polarization, and the activity coefficients.

3.6.1. Temperature polarization

The polarization of temperature limits heat transfer into the liquid phase. According toFigure 26, the temperature polarization coefficient (TPC) drops from 96.5 to 93.5% when therelative length, of the fiber, rises from 0 to 45%. Beyond this value (45%), the TPC has stabilizedaround 93.5%. Also, when we have varied the inlet concentration of salt between 10 and 300 g/l, no effect on the TPC was observed.

In this case, the heat transfer was not influenced by the variation of the salt inlet concentrationdespite the increase in temperature along the membrane module (Figure 27) and “Tam” riseswith the increase of “Ta.”

3.6.2. Concentration polarization

The concentration polarization limits the mass transfer in the liquid film. In order to investi-gate the influence of the inlet concentration of salt on the concentration polarization coefficient226 Distillation - Innovative Applications and Modeling

(CPC), we have plotted in Figure 28 the variation of the CPC with the inlet concentration andalong the module length.As seen in this figure, a very small decrease of the CPC with the increase of the inlet concen-tration of salt is observed. This decrease is due to the decrease of the permeate flux, with theincrease of the salt inlet concentration, which leads to the decrease of “Cam.”

3.6.3. Water activity

The effect of inlet salt concentration on water activity coefficient was examined by varying theinlet salt concentration between 10 and 300g/l. The obtained data shown in Figure 29 indicatethat activity coefficient is almost the same along the module length. This is because of the smallvalue of permeate flow. However, when we varied the inlet concentration, a decrease of 20%for the activity coefficient was remarked. As a consequence, the partial vapor pressure and thedriving force of the MD process decrease, which lead to the decrease of the permeate flux(Figure 30).

3.7. Effect of solar radiation

In order to explain the relation between the permeate flow rate and the direct solar flux, wehave plotted in Figure 31 the evolution of the permeate flow rate with the direct solar flux.According to this figure, we remarked that the permeate flow rate increases with the increaseof the direct solar flux. When the direct solar flux increases, an increasing of the feed temper-ature is consequently reported.

The increase of feed temperature has a small effect on the Reynolds number at a given feedflow rate. The small change is only limited in the density and viscosity of feed. Although theincrease of temperature enhances the Reynolds number somewhat, it enhances exponentially230 Distillation - Innovative Applications and Modeling

the permeate flux. This effect can be attributed to the higher water vapor sensitivity at high temperatures. This causes the increase of vapor pressure difference or driving force ðPH2 O PvÞ.

Figure 32 shows the evolution of permeate flow rate and the direct solar flux during June 21, the permeate flow rate increases in the beginning of the day to reach their maximum toward 12 h and decreases thereafter. This evolution is closely linked to the direct solar flux, which is responsible for this production and therefore has a similar evolution. In order to determine the effect of the initial feed concentration on the permeate flow rate during June 21, we have varied the inlet concentration of salt between 10 and 300 g/l and we have plotted in Figure 33 the evolutions of the permeate flow rate. As seen in this figure, a decrease of the permeate flow rate with the increase of the inlet feed concentration was remarked.

Figure 33. Effect of initial feed salt concentration on the permeate flux during June 21 [56].

4. Conclusions

Distillation process has been in continuous development during the previous decades in order to improve the process efficiency. Therefore, and in order to overcome the disadvantages of the conventional processes, the MD technique has been introduced. This technique has gained much interest, principally, for its lower energy demand and higher rejection factors. In order to improve the MD process performance, many configurations of the hollow fiber have been used. Also and according to some studies, the system efficiencies, of the MD technique, can be improved and its capital cost can be reduced when it is coupled with renewable energy. In this context, we have studied in this chapter the use of the helically coiled fiber in a solar vacuum membrane distilla- tion installation. A mathematical model has been developed in order to describe the evolutions of permeate flow rate with the variation of inlet feed temperature, inlet feed concentration, direct solar flux, and so on. After simulation and comparison between the use of linear fiber and helical- coiled fiber, the results show an enhancement of the temperature polarization coefficient about 6% for the case of the helical fiber. This enhancement leads to obtain an improvement factor by 28% for the helical fiber and to confirm their use for membrane distillation. For the case of the Solar Membrane Distillation: Use of a Helically Coiled Fiber 231 http://dx.doi.org/10.5772/67653

effect of solar energy on the permeate flow rate, an increase of 264% is remarked for the variationof the direct solar flux from 200 to 800 W/m2. However, a reduction of 12% for the permeate fluxis obtained, when the inlet feed concentration grows from 10 to 300 g/l.

[3] Kummu M, Ward P J, Moel H, Varis O: Is physical water scarcity a new phenomenon? Global assessment of water shortage over the last two millennia. Environmental Research Letters. 2010; 5: 1-10. doi:10.1088/1748-9326/5/3/034006